Just when customers finally are making a beeline for auto dealers' showrooms, many of those dealers don't have cars to sell.

The car glut, born of the recession and sky-high interest rates, is dead. The car shortage, created by surprisingly high demand, inadequate production schedules and international politics, is alive and is kicking the stuffing out of potential sales.

Consider the local evidence:

* Fair Oaks Dodge Inc. of Fairfax had to cancel 267 customer orders for 1983 cars this summer. The orders, placed beteween May and August, "couldn't be filled because the cars couldn't be built," said Fair Oaks owner Larry Pateros.

* Salesmen at Courtesy AMC-Jeep Renault in Rockville are happy because of a gamble taken by their boss, Pete Zourdos, at the beginning of the 1983 model year. Zourdos overstocked. "That gave us a good supply of '83's," Zourdos said. "That's getting us through, for the moment. But if we don't start getting some new supplies of cars by the end of the month, we're going to be in trouble."

* Stohlman Datsun of Alexandria has been working with recurring seven-day supplies of new cars--substantially below the more frequent 30-day supply. Stohlman and other Japanese car dealers say they have been hit by a double whammy, a rapidly improving domestic auto market and Japan's "voluntary" decision to limit its exports to the United States to 1.68 million cars a year. "We're seeing a lot of pent-up demand for our product, but we don't have much product to sell," said the dealership's owner, Ed Stohlman.

"Many dealers are watching business walk off the showroom floor because they don't have cars in stock and because people don't want to wait to buy," said Gerard N. Murphy, executive vice president of the Automotive Trade Association of the National Capital Area.

"It seems that it's always feast or famine in this business. On the one hand, when people aren't buying cars, dealers are eaten alive by huge inventory costs. Then, when everybody wants to come out and buy a car, the manufacturers can't seem to build them fast enough," Murphy said. But he added that it's difficult to blame Detroit for its recently cautious approach to production.

A year ago, cars were selling so poorly that domestic manufacturers built only 5.1 million cars, the lowest amount since 1958, when 4.2 million cars rolled off the assembly lines.

But lower interest rates, rebates, and what auto industry analysts say is a genuine renewal of consumer confidence sent sales soaring in the summer of 1983. In the last 10 days of August, for example, domestic automakers sold 191,170 cars to dealers and fleet purchasers, a 15.8 percent increase over 165,072 cars sold in the same period in 1982. The jump marked the 11th consecutive domestic auto sales gain this year.

Luxury, large, mid-size and sports cars led the charge out of the showrooms. Smaller cars and troubled models, such as General Motors Corp.'s X-body cars (hurt by publicity over alleged braking defects in 1980 X's), moved at a slower pace. Buyers, as a result, can expect to pay higher prices for the big and the fancy 1984 domestics, and for many imports--particularly for the Japanese models that could remain in short supply if the voluntary export restraints, in effect since 1980, are extended for another year.

Detroit, meanwhile, is struggling to keep up with growing demand. Domestic manufacturers plan to build nearly 2 million cars in the fourth quarter, the largest fourth-quarter output since 1978, when U.S, automakers turned out 2.4 million cars for the period. A year ago, 1.2 million cars were built during those three months.

"The problem is that, when Detroit was doing its 1983 sales projections, it just didn't think we would have this kind of customer demand, so they didn't build that many cars," said Bob Daly, industry relations director for the National Automobile Dealers Association. "Dealers all over the country are trying to live with shortages."

"It's a problem, but it's the best problem I've had in a long time," said Pateros of Fair Oaks Dodge.

"If you're going to choose a problem in this business, this is the one to choose."