Two separate safety investigations, involving about 600,000 General Motors Corp. automobiles, were announced by the government yesterday.

The investigations, which could take as long as six months before any final action is taken, were disclosed by the Department of Transportation's National Highway Traffic Safety Administration.

One probe involves GM's 1980 X-body compacts equipped with four-cylinder engines and involves reports of engine stalling.

GM, the Transportation Department said, has received 159 complaints about the stalling problem, while the government has received 13 similar complaints from owners.

Included in this study are about 200,000 of the 1980 Chevrolet Citations, Oldsmobile Omegas, Buick Skylarks and Potomac Phoenix automobiles.

The second probe involves 600,000 Chevrolet Chevettes from the model years 1976 through 1980, and centers on complaints that the Chevette manual transmission models experience a "sudden loss of control" when the driver shifts to a lower gear.

Among 116 complaints reported on the Chevette transmission are four alleged crashes, two of which resulted in injuries.

In both cases, the possible defects do not pose a safety hazard, a GM spokesman said last night.

The bulk of the complaints in the X-body cars show that attempts to accelerate a cold engine from a full stop or from slow speeds results in engine stalling, once the car begins moving.

In addition, stalling in these cars is reported to occur after a full stop, when the car slows for a turn, during merges and when moving at speeds between 35 and 50 miles per hour.

The agency said that when the stalling occurs a driver might have to exert more brake and steering effort.