Hello Everybody.
My XJ turns on perfectly, but after a while driving if you don't keep it accelerated, it stalls, I tested the alternator using the "disconnect the negative terminal while the car is running" method. The car immediately went off when I removed it. I guess my alternator is not working, I want to replace it, or should I get a new battery and give it a try?

Thanks in advance.

 

If it drives, take it to Autozone and have them test the alternator and battery. They should be able to do this with the alternator and battery in the Jeep.
If it won't make it there you can remove the battery and alternator and take it to Autozone (or any retail parts store) and have them load test the battery and bench test the alternator.

Check the parts before blowing money on $100+ parts that may or may not be bad. However, if your battery is really old you might want to replace it just for peace of mind.

I'd test and then you can make educated decisions.