I recently began to believe my 4 wheel drive is causing a loss of fuel economy.  It is a 1999 Suburban.  It seems as if the front axle is staying engaged?  Should the CV shafts and drive shaft back to the transfer case be turning, even when the vehicle is in 2 wheel drive?  

Yes, your front axles will turn all the time because they are connected directly to the hub.  Your front drive shaft will probably be turning as well.  There is an actuator on the front diff that disconnects the front axle shafts from each other for 2wd driving.  And yes, your 4wd is causing some loss in mpg. There is nothing, to my knowledge, you can do to change that short of removing your front axle shafts...  

mikesoutdoor:
I recently began to believe my 4 wheel drive is causing a loss of fuel economy.  It is a 1999 Suburban.  It seems as if the front axle is staying engaged?  Should the CV shafts and drive shaft back to the transfer case be turning, even when the vehicle is in 2 wheel drive?

No, the CV shafts will always turn but the drive shaft will not turn is the disconnector is working. By disconnecting one axle shaft, the spider gears allow the drive shaft to remain motionless. That model year used a servo driven actuator so in theory s could get stuck in engaged. 97 and earlier used a thermo based one that was not engaged when power was not applied to it.  

In 1999 the transfer case had a cluth pack in it and the preload on it would turn the drive shaft but not transfer torqe untill clutch pack was engaged, you more than likely have a auto button on the dash and it is normal