NIAGARA FALLS, Ontario (AP) _ Carlos Fajardo took his family across the Rainbow Bridge into Canada and lost the pot of gold that had been their lives in the United States.

Fajardo, who struggled for 20 years to leave his native Cuba, accidentally deported himself and his family by crossing the border on a 20-minute sightseeing trip Dec. 23.

Even though the family lived in the United States for four years, federal immigration officials will not allow them back because they are illegal aliens.

They are stranded in a motel in Niagara Falls, Ontario.

''We came for 20 minutes,'' Fajardo said. ''No one told us we could not go back.''

Fajardo, 39, a small, soft-spoken man, said the ordeal began Dec. 20, when they set out from their home in Miami on a Christmas quest to find snow, which his adopted children, Yoandys, 12, and Yordalys, 9, had never seen.

As he spoke Tuesday, his wife and children sat watching television in their small motel room. He would occassionally turn to the boy, Yoandys, to help him answer in English.

Fajardo said the quest brought them 1,500 miles in their truck to Niagara Falls, N.Y., where they checked into a motel and planned to visit Canada. He told Canadian border guards his family wanted to see the Horseshoe Falls.

When they returned, however, U.S. border guards demanded to see proof of their citizenship. All Fajardo had was a Florida driver's license.

At first, Fajardo maintained that he was a U.S. citizen. Later he said he was a resident alien. But immigration officials, after a search of their records, determined otherwise.

Benedict Ferro, director of the federal Immigration and Naturalization Service office in Buffalo, said Fajardo's wife, Bermaida, and her two children entered the United States illegally in 1985 and that Fajardo entered the country illegally in 1986.

Fajardo denies entering the country illegally.

An immigration judge in 1987 denied asylum to Mrs. Fajardo and the two children. She appealed the decision in August on grounds that she would face persecution if returned to Cuba, but her appeal was rejected.

Fajardo's application for asylum was pending when he crossed the border. His status was officially nullified by leaving the country, Ferro said.

Fajardo could reapply, but his wife and children cannot because they previously provided fraudulent information to immigration officials, Ferro said.

''The family lied and their credibility is about zero at this point,'' Ferro said.

Canadian authorities have given the family permission to stay in Canada until Sunday. What happens to them after that is uncertain.

U.S. Sen. Bob Graham, D-Fla., urged immigration officials to allow the family to return to Florida for humanitarian reasons.

''This family has strong ties to the Miami community through relatives, business and local school attendence,'' Graham said in a letter Tuesday to INS officials. ''It would be comforting to these people for them to be able to resume their well-established lives.''

Under terms of a bond he posted in order to leave Cuba, Fajardo agreed not to return to his homeland. He said he left the country in 1984 with only the clothes on his back.

He achieved relative prosperity in the United States working a number of jobs, including his current one as a boat builder, and said he owns a home in Miami.

It has been nearly three weeks since the family checked into the motel in Ontario, and they've seen more than enough snow.

''We are all very tired,'' he said. ''The children are missing school ... We want to go home.''

Now the family is running low on money, said sister Margaret Quinn of Fort Erie, Ontario, who has been providing assistance through the Niagara Refugee Committee.

Sister Quinn has urged American and Canadian immigration officials to allow the stranded family to return to the care of their relatives in Miami, but says the case seems to be closed.

''It's really contrary to the whole spirit of international law and relations to have them walking about without a country,'' she said. ''This whole thing is really a mess.''