I have a 2007 Yukon Denali and i feel a bumping or delayed reaction in the differential when i start off. This also reacts the same way when i try to pass and the transmission changes to a lower gear. What should i look for???

I would do a pan drop oil and filter change and check for metal in the pan. What color is the trans fluid? Does it smell burnt? Did you confirm the level is correct?

i think i would block the wheels and have somebody go back and forth from d to r and back a few times and see if there is excess play in the trans mount or rear suspension, or driveshaft

Most Denali'* are a full time 4 wheel drive or AWD. If it is AWD I would service the transfer case and look at the oil for metal debris. The AWD transfer case has a differential built into it for smooth turning and better tire wear. Be aware the the transfer case takes a special lube that is blue in color on the AWD models. Sorry I don't have the GM part number handy.

The 2007 AWD transfer case takes ATF, its does not take a special fluid. Thats the AUTOTRAC transfer case, the one with the 4 button dash switch with the top button that says AUTO.

The OP did not even mention if its an All Wheel Drive or a 2 Wheel Drive Yukon Denali, Which is it?

If you have this switch you then need the special AUTOTRAC II Transfer Case fluid. The AWD system has no driver controls.

I am not sure about a 2007 Denali, but earlier versions of GM AWD transfer cases require GM Auto Trak II Transfer Case Fluid GM Part No. 12378508 , which has a bluish color to it. The newer fluid has better friction modifiers. This fluid can only be purchased from a GM dealer. I do know that this fluid solved the chirp problem earlier model of GM AWD vehicles had when turning slowly or backing up and turning.

Automatic Transfer Case (Four-Wheel Drive)
AUTO-TRAK II Fluid (GM Part No. U.*. 12378508, in Canada 10953626).

Transfer Case (All-Wheel Drive)
DEXRON-III Automatic Transmission Fluid.

Note - 2007 NBS All use Dexron VI ATF instead of Dexron IIIH. NOTE - Dexron VI is not backward compatible in transfer cases.