I have a 88 cherokee, and it has the 4.0 out of a 96. I just bought it. It will run good while driving down the road but will stall at random sitting still. Then when I go to start it back up it studers really bad until I tap the gas to get her running again. Then also sometimes I could go to get it it and drive somewhere and it won't start, but if I let it sit for a few minutes it will start right back up! I'm really confused and don't know where to start. I'm new to the jeeps so can anybody tell me where to start?  
Thanks, Mike  

It is hard to say where to start.  Since the motor is from 96 was the computer swapped over from the same donor.  Did you install it or did someone else?  Check all of the connections look for shorts.  If all the computer stuff was swapped over you can have the codes pulled from the PCM.  Don't really know where else to start.  

Double check the conctions on the wiring harnesses.

secontly... you may consider replacing the crank position sensor (CPS). This little thing tends to cause many strating/running issues. I had a random stalling problem with a '96 XJ. CPS was the issue.  

my 2001 jeep did the same thing as yours is doing, it only did it after it was fully warmed, up shut off, then started within a time period of about 20 mins. we never found the problem, so i sold it, to someone special.. lol. , my brothers did the same thing, we were told it was a problem with the crank sensor, changed it and it worked for a year, then back to the same thing. so for shure its the cps.. goodluck with it.  

It could be the CPS, but I have a 01 cherokee that had this problem when idling for extended periods in summer. I was told that the #3 injector gets heat soaked and to insulate the injector and line..must have been the problem because it hasn't happened since.