The Alexandria Redevelopment and Housing Authority is working quickly to find buyers for three rehabilitated houses being sold at discounted prices. If the houses are not sold by Dec. 31, the city could lose state housing funds that help finance loans for the buyers.

Last week, 110 persons took part in a lottery to buy one of the houses being sold under the city's housing rehabilitation program. The large response was greeted with surprise, but most housing officials conceded that the pleasure could be short-lived.

"The houses are a great deal, but there's a real possibility that we may not be able to make the state [loan] deadline [Dec. 31]. It usually takes a couple of months just to complete the paperwork and when we start going down the list, most of the people will eiher not qualify [for a loan] or will not want to move," said Robert Brick, the housing authority's loan coordinator. "But if we don't have buyers by the 31st, state money, which really keeps this program moving, will not be available."

Funds to purchase the houses, priced from $40,000 to $83,000, come from two sources: low-interest loans from the state housing authority and city-backed loans that do not have to be repaid unless the house is resold. A bill now before Congress, which many observers predict will be approved, would severely limit the number and types of loans state housing agencies could make available after the first of the year.

"We've been in the throes from all this [the pending legislation] for a week and a half and we do not know what we're going to do, but we have informed all our branches that they must commit any money they want loaned by Dec. 31," said Anne Clayton, a spokesman for the state housing authority.

The major problem facing the housing authority is time. With previous lotteries, after a buyer was found, processing the loan application usually took at least two months, Brick said. This time, not only does the housing authority have to find a qualified buyer in a short period, it also must complete all the necessary paperwork. And if the last lottery is any indication, housing authorities say they may have problems meeting the Dec. 31 deadline.

Originally, the three houses were among eight offered for sale in a lottery held in March. At that time, 57 prospective buyers applied. But after nearly nine months of contacting the people who put their names in the lottery, trying to find persons qualified for loans and still interested in buying, only five of the eight houses could be sold.

"There is no legitimate explanation for what happened. It had never happened since we first began selling houses in 1978," Brick said. "It was like a deck of cards. Everything took a sudden turn for the worse about a month and a half and ago."

Housing officials said they could not predict the future of the program if state funds should be eliminated or severely curtailed.

"Nobody really knows what's going to happen," Brick said. "We might try to get some other form of financing. Maybe we'll devise our own program. Maybe we'll do something else."