My 2004 jag xj8 is surging at speed of 40 to 65, the RPM goes up and down 200 to 400 rpm.

Maybe a contaminated throttle body.

Is the car equipped with the Automatic Transmission?
If so, read on.
Otherwise skip to the end and answer some questions.

POSSIBLE SCENARIO:
I have observed a condition where my car surges slightly when the torque-converter clutch (TCC) cycles between lock and unlock when driving on an uphill grade.
First some basics and history that will explain why the TCC is used.

Engine, Torque Converter, TCC, and Transmission relationship--
The TCC allows for a solid connection between the engine and transmission which allows the input to the transmission to rotate at the same speed as the engine.
Without a TCC, there is slippage between the engine and automatic transmission. The slippage is greatest at low engine RPM. That is what allows the engine to run with the automatic transmission in gear, like when you first shift into gear or stop at a stop sign. When the throttle pedal is depressed, the engine RPM begins to increase and the torque converter begins to slip less and less the more the engine RPM increases. The car moves. But even at cruising speeds the torque converter slips slightly. Engine RPM is greater than transmission input RPM, which is realized as slight decrease in fuel efficiency.
When acceleration is complete and a constant speed is being maintained, the engine power output is reduced to the point where the TCC can engage and eliminate any slippage between the engine and transmission. If the car has a tachometer the engagement of the TCC can be verified when a slight reduction in engine RPM observed without a corresponding change in vehicle speed.
One method used to test the operation of the TCC is as follows:
Find a flat section of road where it is safe to perform the test.
Reach a steady speed and keep the gas pedal depressed with one foot. While observing the tachometer (or listening for an increase in engine RPM), with the other foot depress the brake pedal enough to activate the break light switch but not enough to engage the brakes. When the brake light switch activates, the TCC receives a signal to disengage. With the gas pedal being held steady, release the brake pedal and the engine RPM should decrease when the TCC engages.
Old cars with Automatic Transmissions did not use a TCC. I believe the TCC was put in use in an attempt to increase fuel economy.

MY EXPERIENCE WITH SIMILAR SYMPTOMS
The condition that causes that issue on my car is this:
- A slight uphill grade increases the load on the engine.
The car tends to gradually slow and it is necessary to depress the gas pedal to maintain speed.
- Depressing the throttle pedal (manually, or automatically with cruise control engaged) signals the torque converter clutch to unlock when the load increases slightly. (A more drastic load increase would signal the Transmission to downshift to a lower gear.) The corresponding increase in engine RPM and output is enough to compensate for the reduction in speed. When the vehicle speed, engine RPM, and throttle position stabilize to the point that the TCC will engage and the engine RPM will reduce in correspondence with TCC engagement. Now, if the road conditions have not changed, power output is not enough to maintain vehicle speed. With the increased load caused by full engagement between engine and transmission, and the cycle (surging) repeats itself until the road conditions change.

Does that help?
If not:

QUESTIONS
Please define the symptoms.
What are the road conditions when the surge occurs? (A slight uphill grade?)
What is the frequency of the surge?
Does the engine power output have a noticeable surge?
Is there a speed change related to the surge?
Does the tachometer move up and down with little or no change in vehicle speed?
Are all instrument indication in the normal range?
What else has changed?

Good luck!

this could be a bad wheel bearing.

pushing the accelerator to the floor causes it to go into clear flood mode .the control module reduces the fuel injector pulse width in order to increase the air to fuel ratio. It could be get to much fuel , leaking fuel injectors or a bad fuel pressure regulator . Pull the vacuum hose off the regulator an see if fuel drips from it , if it does the diaphram has a hole in it .

sounds like the torque converter is going out...I remember on some of the xj8 and xjr models in the x350 class had these issues...the signs were a surge in the rpm cluster at about 50mph and when you attempt to pass or kick down it will ****....but as you get higher in speed it eventually smooths out...This is my insight for your issues...If it was the transmission control module it would throw a definite code.....Usually this issue with the converter was with the earlier vin models ranging in g00 to g400 numbers....and a few others

sounds like its breaking down, check your ignition system, test your leads, check your plugs, check your ignition coils etc etc etc.

Sounds very much like the air mass sensor is not right. This is found on a collar on the air ducting immediately after the air filter box. It ahas an electrical connection running to it. Whilst the engine is warm at running at idle (surge and slow) disconnect the electrical plug. Do not worry this will in no way harm the engine. The engine should soon resume a steady rate. It might be higher or lower than normal but it will be steady. If this happens then it is a certainty that the air mass sensor is at fault and should be replaced.

try to reset the computer if that doesnt work reset the idle speed it may have picked up bad codes

might be ur throttle position sensor

Hi
your problem seems very easy :) hope this one work with your envoy. Just buy AC DELCO carburetor tune-up conditioner.

How you use it: engine running , AC off please

1. detached the big black airflow hose which is attached in the mannifold of the engine block.

2. ask your friend to step on the gas pedal and set the rpm steady in 2000 rpm only.

3. then spray vigorously in 8 seconds the inside circle opening of mannifold while your friend steady step on gas pedal with steady 2000 RPM only.

4. after you spray, let your freind continue on gas pedal with 2000 rpm for 15 more seconds.

5. attached back the airflow big black hose to the manifold and you are ready to roll with your AC on.

if this one doesnt work, please scan your envoy by scanner called TECH II. and find out.