1994 Buick LeSabre cutting off upon acceleration

I just purchased a 1994 Buick LeSabre Limited. The car drove great when I tried it out and for about a week after I got it. One morning it did not want to crank. It would crank, but as soon as I pushed the accelerator it would cut off. It finally started, but I had to baby accelerate so it wouldn't cut off. After a while it started running great again. Ran good for days again and then started the same thing. I have carried it to 2 different mechanics and they can't find what's wrong. The fuel pump checked out ok by the way.It randomly does this, and when it starts, accelerating the vehicle makes it cut off. Any solutions, suggestions

Welcome to AF, when the condition occurs is when the fuel pressure should be tested.