Has your General Motors car's transmission conked out, leaving you with a $600 repair bill? Does the car have a history of being difficult to start, emitting black smoke or running rough, all of which are possible signs of premature camshaft wear? Did the fuel pump on your GM diesel rust out and cost $300 to $700 to replace?

If any of your answers is yes, you may be eligible to recover all of your costs through free mandatory arbitration under a proposed agreement between GM and the Federal Trade Commission.

The agreement, which was announced last week, is scheduled to take effect after a 60-day public comment period.

It is an unprecedented agreement that settles a 1980 complaint by the FTC that charged GM with failure to notify consumers about these serious problems or defects in certain GM cars.

The FTC has received more than 20,000 complaints about problems with engines and transmissions that were installed in more than 21 million GM cars--or nearly half of all GM cars and light trucks produced--since 1974.

Under the terms of the proposed agreement, affected GM car owners would be entitled to receive:

* Arbitration of their complaint within 60 days after they requested arbitration and a decision by the arbitrator within 10 days after the hearing.

GM would be bound by the arbitrator's decision, but the consumer would have the option of taking his case to court. The arbitration would be conducted by independent arbitrators and would be arranged by Better Business Bureau offices around the nation.

* GM Product Service Publications containing information on repair, maintenance and care of cars and light trucks for the model years 1982 through 1991. GM previously has sent the PSPs to dealers only. More than 200 PSPs are published annually by GM. The company has agreed to index the publications so that a consumer could look for his particular type car--for example, a 1982 Oldsmobile--and then request the PSPs with information about that car type.

* Fact sheets on the specific auto components that have caused problems in the GM cars, namely, THM 200 automatic transmissions, V-8 engine camshafts and diesel fuel pumps.

Under the proposed agreement, GM would mail notices about the availability of the arbitration, PSPs and fact sheets to all consumers whose complaints are on file with the company or with the FTC.

Any consumer who has had problems with his GM car or who wants to verify that his name is on a list to receive a letter from GM should contact the FTC's Cleveland office at 118 St. Clair Ave., The Mall Building, Suite 500, Cleveland, Ohio 44114. All inquiries should include information about the type of GM car with which you had trouble and the types of problems experienced.

GM agreed to the settlement without admitting any wrongdoing, any defects in its products or any pattern of problems.

Here is what consumers say happened to them, according to William W. Jacobs of the FTC Cleveland Regional Office, which negotiated the GM settlement:

* Transmission problems. Some THM 200 automatic transmissions, used in 5 million to 6 million GM rear-wheel-drive cars made since the 1976 model year, have failed completely, with all gears going out at once, while others have leaked transmission fluid while continuing to operate.

To determine if your car has a THM 200 transmission--one of about 10 basic GM transmissions used in cars and light trucks--check to see if the word "metric" is stamped on the bottom of the transmission fluid pan. Repair bills for the THM 200 transmissions typically amounted to $400 to $600, the FTC said.

* Premature camshaft wear. This problem, which has been attributed to using the wrong motor oil, involved camshafts used in 15 million 305- and 350-cubic inch V-8 engines produced by the Chevrolet division beginning in 1974.

A bad camshaft means that the valves don't open and close properly, so the car may run rough, emit black smoke or be difficult to start. Camshaft repair bills generally are more than $400, the FTC said.

* Diesel engine fuel pumps. The FTC charged that a design problem in the fuel-injection pumps and fuel injectors in some of the 500,000 350-cubic diesel engines manufactured by the Oldsmobile division since 1977 has made them susceptible to water damage and leaving owners with repair bills that ranged from $400 to $700, the FTC said.