After i installed the supercharger and an AEM Fi/c i started to have the following problem! When i drive for about 10 miles the jeep starts acting like the following video!

Search for members here named Cobramarty and boostwerks, they're the SC guys to help you out.

Ya know OS, it may be time to open a really modified jeep section because these question are becoming common. Supercharging a jeep and what not. Just saying.

It could be SC compressor surge.
Do you have a SC bypass valve in place?

Nope i don't have such a thing. But it only does this when it gets hot. I have changed almost every sensor, nothing happened! Now i am planning on changing the map! i heard that it might be the problem!

Only map and the sensor on the intake manifold left to change!

I doubt that any sensor or map changing will make a difference.
Check for any vacuum leaks.

My kits all have a SC bypass valve to prevent compressor surge. During idle and high vacuum, the valve is open and air after the TB bypasses the SC and goes directly into the intake manifold. This keeps the SC cooler and because it is not compressing air, it free spins and uses minimal power like 3-5hp and hence doesn't cost any mpg while cruising out of boost. With low vacuum, the valve closes and all air goes thru the SC.

Still check for vacuum leaks.

Typically this type of behavior is related the idle air control valve.

Do you have resistors installed for the injectors?

Wideband gauge?

I'd check the short and long term fuel trims as well. It is more than likely bouncing around trying to hone in on 14.7 but if the fuel corrections are to large it will fluctuate rich to lean causing the RPM's to fluctuate as well.

I'd honestly recommend taking it to a local tuner if possible

Well, the problem is that i am going blind cause there is none here who can manage it. I have already tried a lot of them and they don't seem to understand it! Another thing is that when i stop driving and leaving my xj just idling. When i pop up the hood and it starts dropping temperature it slowly stops acting like this. I also unplugged the map and everything almost went back to normal. Tomorrow another xj is coming in my hands and i will try the map from it. Hopefully it will fix the problem.

I have changed that too. No difference!

I will start looking for vacuum leaks tomorrow i will change all the tubes! But the problem starts when my xj is getting hot. That brings up the problem. just searched for the bypass valve. i am sure i don't have one. Is there anyway to install one?

If your doing this yourself, you will need a wide band gauge. It is more than likely a fueling issue.

Have you watched the maps under real time while it does this? You'll want to know exactly what cells it is bouncing around in. If there is a large difference between those cells, it can cause this issue. It's essentially bouncing between target values

Okay so then it is likely a tuning issue. Tuning is key on any forced induction platform.

well the map i have made was working just right. But the problem begins when it gets hot. When i open the hood after a while it stops bouncing and the throttle works correctly! I think i have a map sensor problem! is the only thing i have not changed. It might got burnt out! I have a wide band installed together with an AEM Fi/c! I talked with AEM and i don't need resistors for the injectors.

Which model AEM? 1910 or 1913(chrysler specific)