Our 2004 X5 exhibts a mild to moderate jerking

have transmission checked

Auto or manual? if auto then a change of the transmission fluid & filter should do the trick

run the fault codes to check for problem servos and solenoids . Possibly a change of transmission oil would help. At 80mph you should be in OD so there would be no more servo /solenoid operation until you slowed down and the bands and clutch packs are again being used.. A band clutch pack adjustment may also be in order as out of adjustment will also cause jerky / slap on changes.

Take to a transmission shop, likely you need overhaul or replacement.

If the problem is due to warped brake discs, you will typically feel a mild pulsing in the peddle when braking firmly. Also, when you are experiencing this shudder, taking your foot off the brake (when safe to do so) should cause it to stop. If that is not the case, I would consider again the transmission. I am on my second Caravan, so I speak from experience. The Caravan transmission should have the fluid changed every 30,000 miles to keep it in top performance, especially if you are carrying any heavy loads or pulling a trailer. When you are slowing to a stop, the transmission must downshift through each of the gears. If it stays in the higher gears at too slow a speed, you will feel a shudder. Sometimes this can be corrected by changing the transmission fluid. Be sure to use the proper Chrysler fluid for your transmission. Typically it is the highest (overdrive) gear that causes the shudder. You can determine this by moving the gear selector from "D" to "3" when you are experiencing the shudder. Other possibilities are alignment, worn stabilizer bar bushings, worn ball joints, and out-of-round tires. Most of these also involve some accompanying noises though. Good Luck.

That is the speed when it would normally shift into overdrive or the torque converter would go into lockup.
It is also when the engine would be working hard and a slight miss could be magnified.
You may want to have a transmission shop test drive it for their opinion.

This type of issue requires a test drive by a professional.

Your transmission fluid is dangerously low (tranny is dry). The pops & jerks are the transmission
internal components trying not to seize onto each other due to lack of lubrication and/or overheating.
Low transmission fluid leads not only to loss of lubrication but lots of overheating (of the tranny).
The loss of Elantra performance (speed tops out at 55), is caused by power loss due to friction inside the transmission. All your power is lost overheating the transmission (toward destruction), instead of
being transmitted through the transmission to the wheels.

The 2004 Elantra takes Hyundai SP-III Automatic Transmission Fluid, with 8.4 quarts used in a
total refill - but just 5 quarts at a fluid change. For How-to transmission fluid change instructions:

http://en.allexperts.com/q/Hyundai-Repair-815/2004-Elantra-GT-transmission.htm

www.autozone.com claims that 2004 Hyundai Elantra can take these non-Hyundai ATF's:
Lucas Semi-Synthetic Multivehicle ATF
Pennzoil Muilt Vehicle ATF
Valvoline Maxlife Dex/Merc ATF
Castrol High Mileage ATF

Your transmission is slipping which can cause a huge amount of damage both to the car and your wallet. Take it in for service as soon as you can.

It's a step-by-step process. If it only happens on acceleration then it is a drivetrain problem. Start verifying from the outer cv joints and go in from there