Smoke comes out underneath after having four wheel drive engaged & driven for awhile

need to have transfer case or axle check for damage

no year car.
no model jeep stated.
now 4wd option stated (
command trac, Select track. quadra-trac/drive?,)
or if unknown what transfer case is there (tag on rear says)

the front axle have the vacuum valve on it.
does it work, the vacuum servo ( test it?)
if no vac. servo there, that is the newer jeeps.

is this your jeep?

Check the soildnoid that engages 4x4 by switching it from 2 to 4 wheel drive and listen to it 27 dollar part if needed to be replaced

need to look under at the drive train and check the c/v joints the transaxle case seals etc noise can be anything from bearings to gear or seals failing

Most vehicles with four wheel drive and positraction in the rear will have an "open" style differential up front. (unless modified for off road only use). An open diff will only spin the wheel with the least traction. The only way the other wheel would have spun is if that happened.
Reason front posi units aren't used on the street is that they make steering difficult.

To engage the four wheel drive, while rolling, pull the lever back one notch and that will engage the transfer case. You can easily do that up to speeds as high as 35mph. Pulling the lever all the way back will put it into 4 low which is not often used and may grind if it does not engage right away. That really doesn't matter much because that gear is only used for pulling heavy loads at low speeds. (I use mine about once every two years) If you do need to use it, generally you can engage it with the engine off without problems. The neutral position is used to disengage the wheels if the vehicle needs to be towed. If it fails to disengage, often backing up about twenty feet or so will help.

With low miles such as you have, It would be expected that the four wheel drive should not fail. Especially if it is not frequently used.
your vehicle has a quadratrac system which simply means it operates in two wheel drive and engages 4 wheel drive when the rear wheels begin to slip. The device that enables that to happen is inside the transfer case...It is called a fluid coupling. You have another similar device that you can see...the clutch device on your mechanical fan. The coupling is filled with a grease that expands and drives the locking mechanism. Expansion is caused by heat (caused by slip in the rear).
Sounds great, but often the grease escapes causing a malfunction. It can also be damaged by unequal tire heights.
A transfer case is not user friendly when it comes to rebuilding. (unless you have experience)
Things you can check are the lube level in the transfer case, also try to clumb a steep slippery grade and have someone watch to see if the front wheels engage. If not check the axle joints and make sure the front differential is turning the front axles (wheels off the ground, turn each wheel while someone holds the other and see if the driveshaft turns.) if everything looks good then likely the problem is inside, likely the coupler.
As far as how low gear works, some I've seen get difficult to engage from lack of use. But, if the transfer case is in need of work that is all part of the same unit so it does not matter. Low is used for driving very slow pulling a heavy load.
I can't tell you exactly what's failed because I can't see/hear it. but I hope the info I gave you helps you to understand and do some checking.

Sounds like the splines on your transfer case gear are ground down

I take it the transfer case shifter feels okay (shifts through all four gear positions), so try jack up one side of front end, rotate wheel while looking in knuckle to see if drive axle turns, if it does, then hubs engaged. Now if someone holds the front d shaft, and wheel won't turn, then both hubs are engaged. Next put t case in 4xhi or 4xlow, if you cant turn the wheel, then the t case is engaged, and all is normal. If wheel still turns at this point, then the t case is not engaged for some reason, but post again if it does. Hope this helps.

First, get it onto some dry ground and look underneath. See if you can get an eyeball on whats making noise. Without lying underneath, have someone try to engage 4x4 while you watch from the side.Or get it up on a lift. When you have an idea what or where noise is coming from, I can help you with the how to fix it part.