1993 Ford Probe Bogged down during acceleration

Engine Performance problem
1993 Ford Probe 6 cyl Front Wheel Drive Automatic 110k miles

I have a 1993 Ford Probe 2.5L engine. The engine bogs down during acceleratioin to the point that it sounds like its stopped, and then it will blow out the exhaust violently. 2 mufflers were blown wide open by this problem. The other thing is that sometimes it will have the problem at start up and other times after the engine warms up, but if it's on for 5 minutes the "missfire" will occur. I notice that if I accelerate very slowly and gradually it will not happen or when it's already moving, only when I try to accelerate from a normal stop. Is the car sucking in too much air? Why would it blow the muffler wide open? The problem happens in park and in gear, always during acceleration, idle is fine.