General Motors Corp. and Ford Motor Co., battling to better their positions in a convalescent domestic auto market, both announced new 8.8 percent financing programs yesterday.

The interest-rate war primarily will affect sales of small cars and trucks, many of which have been left on showroom floors behind faster selling larger models.

The new GM and Ford programs, both of which are scheduled to last through June 30, probably will be matched in some way by Chrysler Corp. and American Motors Corp.

"We intend to remain competitive," Chrysler spokesman Tom Houston said yesterday. However, until June 10, Chrysler will keep in place the 9.8 percent financing plan affecting most of its 1982 and 1983 models. The Chrysler plan, in effect since April 11, also gives customers the option of accepting rebates from $300 to $750 in lieu of low financing rates.

GM's 8.8 percent plan, to be administered by General Motors Acceptance Corp., applies to the Chevrolet Chevette, Cavalier and Citation; Pontiac 1000, 2000 and Phoenix; Oldsmobile Firenza and Omega; Buick Skyhawk and Skylark; Cadillac Cimarron and Chevrolet S-10 and GMC S-15 pickups.

The financing rate will rise to 9.9 percent on July 1 and that rate will expire on July 31, GM officials said yesterday.

Buyers of the Chevette, Pontiac 1000, S-10 or S-15 can accept a $300 rebate instead of low-rate financing.

Ford's 8.8 percent program basically apllies to sales of its Escort and EXP, and the Lincoln-Mercury Lynx and LN-7. Ford also will offer cash rebates in lieu of low rates, at customer request, a Ford spokesman said yesterday.

American Motors Corp., No. 4 behind GM, Ford and Chrysler, is keeping in force a dealer incentive program that awards discounts to dealers who buy large numbers of AMC's slow-selling models. Those cars include the four-wheel-drive Eagle, and the moribund Spirit and Concord passenger lines, which will be interred at the end of this model year.

AMC dealers can, if they desire, use their discounts to knock down the sticker price on the slow-selling models. But customers seeking AMC's hot-selling Alliance can expect to pay the full cost of that car, the daily production of which rose from 300 units in June 1982 to 900 units in mid-May 1983.

AMC is adding two weekend overtime shifts at its plant in Kenosha, Wis., to help keep up with demand for the Alliance, AMC spokesman John McCandless said yesterday.