But Ghazi Ibrahim Abu Maizar, whose stone-throwing in Hebron led once to his arrest, and Lafi Khalil, whose family lived in a quiet village called Ajoul, near Ramallah, had one thing in common, according to those who knew them then -- a determination to go to the United States.

Now, as they lie wounded in a Brooklyn hospital, accused by the authorities of conspiring to terrorize New York and the nation with suicide bombings, Mr. Abu Maizar, 23, and Mr. Khalil, 22, have become the focus of a mystery: Did their paths cross halfway around the world by chance or by design? Did they come to America to seek a better life, or to slaughter for Palestinian vengeance?

As Federal prosecutors arraigned the men on bombing-conspiracy charges and as security at buildings and transportation hubs across New York was intensified, investigators sought this weekend to determine the scope of the plot -- who was involved, and whether it was a case of amateurs working alone or more deeply committed terrorists with links to Hamas or other radical Islamic groups.

But for relatives and friends of the accused men, there was only stunned disbelief over the arrests before dawn Thursday at their Brooklyn apartment -- and a host of questions about how two quiet, polite young men who seemed to care little about religion or politics, who called home regularly to tell of girlfriends and their improving lives in America, could have become would-be killers.

''He was a balanced person who had always been friendly with everybody,'' Suhail Mifleh Khalil said of his nephew, Lafi. ''Maybe he was blackmailed or cheated. I am in shock.'' In Ajoul, the village where Lafi Khalil grew up, he was a good student, always on the honor roll, and had never been in trouble, his uncle said. His father drove a semitrailer.

Village life in Ajoul seemed to reflect the tempo of Ramallah, the nearest town, 10 miles north of Jerusalem, traditionally a quiet, relatively prosperous community where many Palestinians are Christian, where a Western life style is common and where Palestinians and Jewish settlers mostly keep their distance.

In contrast, Hebron, an old town 20 miles south of Jerusalem, where Mr. Abu Maizar was raised, has long been a battleground of the most extreme elements of Islamic fundamentalists and Jewish settlers. During the Intifada, almost every Palestinian youth in town hurled stones at Israeli troops, and Mr. Abu Maizar was among them in 1990, when he was arrested and held for a week, though not charged.

His brother, Nour, 33, a lawyer, said Ghazi was the youngest of seven children in a well-educated middle-class family touched repeatedly by the Israeli-Arab conflict. Two decades ago, he said, an auto parts store owned by an uncle was blown up by Israeli soldiers amid clashes between Palestinians and Jewish settlers, and Nour Abu Maizar was himself deported by Israel briefly for Palestinian political activities.

Ghazi's only political leanings, Nour said, were for the Popular Front for the Liberation of Palestine, one of nine factions that make up the Palestine Liberation Organization of Yasir Arafat. But aside from the stone-throwing incident, he had had no serious involvement, his brother said. Another brother, Nasser, said that the whole family supported the peace treaty with Israel.

Ghazi did not seem interested in religion or politics. ''He left Hebron to get away from the suffering of the people living here,'' Nour Abu Maizar said. ''He was looking for a good future for himself.'' What he and Mr. Khalil wanted, their families said, was to go to the United States.

Roundabout Voyages To Same Destination

Their separate trails from the West Bank to New York were tortuous. Mr. Abu Maizar left Hebron in 1994, traveling first to Canada, where he lived in Ontario and British Columbia. He studied English in Toronto, but did not enroll in a business administration course in Ottawa as he had hoped. He worked at odd jobs in both cities, and twice in 1994 was convicted of crimes in Canada, first simple assault and then using a stolen credit card. Each time he was sentenced to a year of unsupervised probation, according to an official in the United States Justice Department.

Nour said he occasionally sent his brother money in Canada -- $2,000 the last time, about six months ago. Mr. Abu Maizar tried to sneak into the United States from British Columbia -- twice in June 1996 and again last January. He was seized by immigration officials in Washington State, but was released in February, pending a further hearing, after Canada refused to take him back because of his criminal conviction.

At an immigration hearing in April, Mr. Abu Maizar asked for political asylum, saying Israel wrongly considered him a member of Hamas and would persecute him if he was sent back. But in June, he withdrew that request and promised to leave the United States in 60 days, by Aug. 23. It was unclear if he intended to keep this promise. In any event, he left Washington State and headed for New York City.

Mr. Khalil, for his part, left Israel last November, moving first with his family from Ajoul to Aqaba, Jordan, then traveling alone to Mexico. He reached Los Angeles on a visitor's visa, but did not leave the United States when it expired in December. Instead, his uncle said, he went to Cleveland and later to New York, paying his way by working in supermarkets and at odd jobs. He faced deportation if caught.

Like many migrants from the Middle East, both men gravitated to the Atlantic Avenue area of Brooklyn, where muezzins call worshipers to mosques, Arabic is spoken in many shops, newspapers and other publications in Arabic are sold and dozens of restaurants offer Mediterranean and North African specialties.

Mr. Khalil was ill and had little money when he arrived in Brooklyn, his uncle said. ''When he first went to Brooklyn his financial situation was not good,'' he said. ''He was ill and there was no one to take care of him. He may have gotten involved with the wrong people who took advantage of his needing a place to stay.''

Varying Accounts Of a Fateful Meeting

It is unclear where and how Mr. Abu Maizar and Mr. Khalil met. One account suggested it was in North Carolina, as recently as a week ago. Other accounts suggested that they had lived together much longer, along with a shifting number of other Middle Eastern immigrants, in three grimy rooms on the ground floor of a two-story shack hidden behind a store at 248 Fourth Avenue, between President and Carroll Streets on a commercial-industrial fringe of Park Slope.

The place was a study in squalor. There were no furnishings beyond a couple of mattresses on the floor and a television set. In one room, what appeared to be a prayer rug was tacked to the wall. In the kitchen, a sink lined with scum was piled with dirty dishes. The refrigerator was bare. Flies buzzed everywhere.

It was a secretive life, as well. Neighbors and shopkeepers saw the men come and go at all hours of the day or night, sometimes carrying boxes or suitcases, sometimes vanishing for days, making calls from pay phones several times a day, rarely having more than cursory conversations with people, living mostly on rice and milky tea bought at nearby groceries and delicatessens.

Mr. Abu Maizar worked as a grocery clerk and at a variety of handyman jobs but had no regular employment, according to Raj Singh, the proprietor of Tina's Grocery, where the men often shopped. Mr. Singh said Mr. Abu Maizar sometimes stopped to chat, and spoke of wanting someday to own a grocery store.

Occasionally, the men ate at the Pitaria Restaurant on Atlantic Avenue. Ahmed Nabawy, the owner, an American of Egyptian origin, remembered them.

''They looked like good people,'' he said. ''They appeared to be quiet, just regular people.''

On Fridays, neighbors said, some of the men from the apartment went to services at the Masjid Al-Farooq, a mosque on Atlantic Avenue, but leaders and members of the mosque said they had never seen Mr. Abu Maizar or Mr. Khalil at their Sabbath services.

Mr. Abu Maizar's family in Israel said that while he called home twice a month and wrote letters regularly, he never mentioned that he was living with a Palestinian. In his last call, about a week ago, he said he was in Florida at the home of a new American girlfriend and that he planned to bring her home to meet the family before proposing marriage. He sounded ebullient.

A similar call from Mr. Khalil was received by his uncle, Suhail Khalil, about three weeks ago. ''He was fine, sounded happy,'' the uncle said. ''He told me he had plans to marry an Arab-American.'' It had been his nephew's dream to get a green card and work in America, Mr. Khalil said. But neighbors, shopkeepers and a building superintendent noticed odd goings-on at the men's apartment.

Getting Down To Ugly Business

''They were bringing in boxes all the time,'' Nicholas Fialo, the superintendent, recalled. ''One guy says, 'I got a bomb in here. I'm going to blow up the whole building.' '' Another man ''came in with a piece of pipe a good two to three feet long,'' he said.

Later, the superintendent said he found that the men had discarded the shells of television sets and videotape machines, their electronic components having been removed. He said one of the men had a beeper and would respond to it by going out to make four or five calls a night from a pay phone.

Last week, Marisol Rodriguez, who works at a Park Slope hardware store, said Mr. Abu Maizar had bought six feet of wire, a quantity of electrical tape and three large lantern batteries, and added: ''He took all we had and then he wanted to know if we had more coming.'' At the Family Car Service, the business that occupies the store just in front of the men's apartment, a dispatcher who identified himself only as Carlos D said the tenants in the back over the last 10 days had brought in a series of bags and boxes. ''I would never see the same people,'' he said. ''They were different people at all hours of the night.''

Behind their locked door, the authorities say, the men were making crude bombs and conspiring to terrorize New York and the nation by detonating them in crowded subways and buses, killing themselves, too, in apparent emulation of suicide bombings that have wracked their homeland. The latest killed 15 people, including 2 suicide bombers, in a Jerusalem marketplace on Wednesday.

On Wednesday afternoon, Nelson Gonzales, the owner of a delicatessen a few doors away on Fourth Avenue, said Mr. Abu Maizar, whom he recognized as a regular customer, came in and asked the proprietor to turn on the Cable News Network on his store television. He did so, he said, but there was no immediate report on the bombing in Jerusalem, only a business report.

''No, that's not what I want,'' Mr. Abu Maizar was quoted as saying. He sat there a minute, apparently impatient, then left abruptly, Mr. Gonzales said.

Before dawn on Thursday, a squad of flak-jacketed police officers, acting on a tip from a man who said he lived with the two men and knew about the plot, raided the apartment and shot Mr. Abu Maizar and Mr. Khalil, saying they feared one of the men scrambling in the dark was about to set off a bomb.

Mr. Abu Maizar was shot twice in the right leg. Mr. Khalil received five wounds. Both were taken to Kings County Hospital Center where they were listed in stable but guarded condition and arraigned in their beds. A third man who was taken into custody at the apartment was held for questioning, but was not immediately charged with a crime.

Besides two pipe bombs in the raided apartment, the authorities said they found anti-Israel propaganda, bomb-making instruction manuals and Mr. Abu Maizar's application for political asylum -- ironically claiming, as a basis for staying in this country, that he could not go home because he had been branded by Israel as ''a member of a terrorist organization.''

Photos: The house in which the two bomb suspects were found. (Reuters)(pg. 29); Children play in front of the house in Hebron, 20 miles south of Jerusalem, where Ghazi Ibrahim Abu Maizar grew up. In 1990, he and his compatriots threw stones at Israeli troops. He was arrested but not charged. (Rina Castelnuovo for The New York Times); Lafi Khalil, third from left in the back row, is shown in a 1996 family photograph at his home in Ajoul, a small town in the West Bank. Mr. Khalil was shot in Brooklyn by the police, who had gotten a tip about a bomb plot. (Associated Press)(pg. 30)