General Motors Corp. yesterday delayed the introduction of its 1980 models by two weeks as the auto industry searched for new ways to unload its backlog of unsold cars.

Additional incentives to move big cars, which possibly could include cash rebates to customers, reportedly are under discussion at all three of the big car makers.

Already paying dealers up to $700 for every hard-to-sell model they can move, GM gave its dealers more time to clear their storage lots by stalling from Sept. 27 to Oct. 11 the start of the new model year.

"Of course Chrysler will do likewise," said one executive of the number three car maker. Chrysler had not officially announced its new car debut date.

A Ford Motor Co. press officer said Ford still plans to bring out its 1980 line on Sept. 28.

In a related development yesterday, Ford announced it will guarantee its cars and light trucks against rust for three years. See story on page F5.

GM said it was postponing the birthday of its 1980 cars to give dealers "more time to make an orderly cleanup."

The industry's supply of unsold cars averaged 72 days worth - only 12 days more than is considered normal at this time of the year. But the backlog stretches to 150 days' sales of some full-size models.

The backlog is far bigger than when the original Arab oil embargo hit in 1973-74, because that gas crisis came in midwinter, when dealer stocks are normally low.

The auto companies responded in 1974 with direct rebates of several hundred dollars to car buyers.

But the industry is reluctant to return to rebates. "Nobody wants to be the first," said one auto company executive, who explained that "a lot depends on how the incentives now in the marketplace work."

The current strategy is to give rebates to dealers, who generally pass the money on to consumers by cutting car prices.

General Motors has the most aggressive dealer incentive program, paying dealers up to $700 for every full-size car sold. "They haven't put money like that into the market since the oil embargo," said an executive of a rival automaker.

Special deals to dealers are normal at this time of year, as the auto industry ships the last of its old models and prepares to begin production of new ones.

The Associated Press reported yesterday that both Ford and GM are delaying the startup of production of some 1980 models. Ford has moved the schedule back three weeks at one factory and two weeks at three others. GM extended the usual summer shutdown by an extra week at its Cadillac plant in Detroit, a Buick factory in Flint and the Oldsmobile facility in Lansing.

In addition to giving dealers more time to sell their '79s, the delay in new-model introductions will give the auto companies more time to assess what's happening in their business.

Whether sales are slumping temporarily because of gasoline shortage and will come back quickly as they did in 1974, or whether they are down for a longer term because the nation is moving into a recession is unclear.

Car sales have slipped for three months in a row and in June were 26 percent below a year ago.

In the Washington area the slump so far is less severe, with motor vehicle registration figures showing sales are off 18.5 percent in the District of Columbia, 16.8 percent in Virginia and 16.6 percent in Maryland. CAPTION: Picture, The Toyo Kogyo "Ujina" automobile assembly Plant. AP