The number of existing houses for sale in the Washington area has fallen dramatically in recent months, and properties that come on the market are being sold at a pace reminiscent of the late 1970s, according to local agents and brokers.

Agents in the suburbs say they are beating the bushes for more homes to show to prospective buyers. "Anything that's really good sells very fast," said an agent in the Fair Oaks area.

The Northern Virginia Board of Realtors reports that the number of homes for sale on its multiple listing service is roughly half what it was a year ago, and the number declined by about 25 percent between January and March.

A Fairfax City family was surprised this week when someone walked in off the street and offered to buy their home, which wasn't on the market.

"The people walked in and said this was the sort of house they had been looking all over the area for," said Carol MacNeil, a Fairfax City real estate agent with Red Carpet. It was an offer the Fairfax City family couldn't refuse, and now MacNeil is trying to find a town house for them after their spur-of-the-moment sale.

This episode, which took place early this week, is unusual, perhaps, but illustrates the current situation.

A strong economy and stable interest rates have lured buyers back into the market and kept them there, agents say.

"Those people who sold their house will be buying a new town house and living in it for six months and then look for something in the $250,000 range," MacNeil said.

In addition, strong demand for new homes is beginning to stretch out delivery times for them, encouraging buyers in a hurry for housing to seek existing dwellings.

Beyond lamenting lost sales opportunities, however, brokers and agents aren't complaining. Not long ago, even attractive, well-priced properties could languish on the market for many months. Early in the economic recovery that began at the end of 1982, it appeared that there might be more pent-up demand on the part of sellers than of buyers.

At one point in 1983, more than 40,000 properties of all kinds had piled up in the multiple-listing services of local boards of Realtors.

Today, although poorly maintained, dirty or overpriced houses still sit, attractive ones usually sell within weeks, and sometimes within a day or two.

"We are very enthusiastic about this market. What we have is going very quickly," explained Saralee West, head of the Merrill Lynch office in the West Springfield-Burke area, where inventories are behind sales. "It is difficult to keep the inventory up," West said.

Sally Swanson, an agent with Laughlin Realty in McLean, said sales are good in the Great Falls/McLean area and listings are way down.

"I have customers in several price ranges, and I don't have any homes to show them. I have run out. Many homes sell before a listing even hits the computer," Swanson said. She was referring to the Northern Virginia Board of Realtors' multiple listing service.

"What we really need is more listings," said a Montgomery County broker.

Homes in the $200,000 to $300,000 price range in good condition are especially hard to find in the Potomac, Great Falls, Vienna and McLean areas.

Older split levels, built with plaster walls and other structural features not found in homes built today, may be all it takes to get a signature on a contract these days, said several agents.

Another agent complained of looking for a four-bedroom house for a family in the Vienna area for days and finding "absolutely nothing in the $140,000 range."

Statistics from the Northern Virginia Board of Realtors indicate a steady decline in inventories along with increasing sales since January.

Inventories are far behind the demand for housing this year. Current stock is way behind figures for comparable periods of 1984, according to Joseph Hayden, a spokesman for the Northern Virginia board.

George Fulton, a real estate consultant who does work for Long & Foster, said that in addition to brisk sales, one of the major factors figuring in the low inventory is the relatively small number of homes, especially for the move-up market. During the high-interest recession years of the early 1980s, builders concentrated on town houses and other lower-priced homes catering to first-time buyers.

"Now those people are moving out" and looking for move-up houses. "The overall demand has increased," he said.

Fulton said the increased delivery time now prevalent in this area for new homes is adding "more pressure to the inventory of resale houses. Delivery times often are running more than six months forconstruction of a new home.