I have a 1983 delta 88 with a 307 and a rochester quadrajet. When I crank the car it seems like its going to stall then it gets to normal and when I am pressing the brakes slowing down the car seems as if its going to stall wat is the problem?

 

Is the choke operating and set correctly? When was the last time it was tuned up? What is your idle speed and timing set to? Are the vacuum and mechanical advance working properly?

 

If the engine seems to knock and chuggle and strain like slowing down a manual shift car without pushing the clutch in, suspect the torque converter clutch solenoid not releasing. I think this was widely used in 83.
If it seems to just run out of power and no extra effort is needed on the brakes, then that would not be the problem.

For troubleshooting, the TCC can be disconnected by unplugging the connector to the tranny.

 

If pressing the brakes causes the car to stall, check for vacuum leaks. Also, the CCC system on your car is VERY VERY VERY (can I say that enough?) sensitive to misadjustment, faulty sensors, and vacuum leaks. You MUST have the system adjusted following the detailed procedure in the factory service manual. And yes, if the system only stalls after you've been driving and THEN press on the brakes, have the torque converter clutch checked.

 

I agree with the above statement on vacuum leaks.

Will the car try to stall if you mash the brake while idling in gear?

If so, the brake booster could be letting vacuum escape. It can be checked by unplugging the vacuum line to it and plugging it, then repeat above test (don't drive it this way, you wont have power brake assist).