My 2001 Yukon Denali will not stay started. It starts and then it cuts off. I have changed the alternator along with the battery.

sound like battery has weak or battery terminals and post need cleaning. have battery charged and checked, if battery good. alternator not charging battery. if battery over 5 years old more likely battery is bad.if battery too weak head lights wont turn on battery dead this time of year if battery old. cold weather will finish it out.

You probably interrupted the antitheft system. This link explains.

http://vatspasslockpasskeysecurityhelp.yolasite.com/

Alternators wont cause a starting problem. so it cranks? or not? cranks but wont run? the first thing to verify is fuel pressure. If its not 55-60 psi, it will not run. you may need a fuel pump.

Hi there !

I won't say its an alternator problem because the alternator only charges the battery when its on, And it should start with the jump cables even if the battery and the alternator are bad. your Issue is not clear. Does the car start when you jump it ?

Hi, there is a park relay in middle of the interior relay box under the dash to the left of the steering column. This is shown on page 6-61 of your owner's manual (http://www.extendedgmwarranty.com/owners-manual/gmc/2001-GMC-Yukon-Denali.pdf)
With the battery connected, pull out the relay and push it back in. If it clicks when you do this, the headlight switch is bad. If it doesn't click, the relay is bad. Try swapping the relay with another similar relay, such as the horn or A/C relay. If that solves the problem you need a relay. If not, you need a switch. Please let me know if you have any questions, and thanks for using FixYa.

Anti-theft system problem ? Security light lit on the insturment cluster ?

Without testing the fuel pump electrical circuit there is no way you could be I'm pretty sure its the fuel pump Testing Electric Fuel Pump Problems with Voltage Drop Test
GM Fuel Pump Relay Testing

check fuse box under hood for alternator fuse /relay and check check all of them that go to ignition/starter......

THE BELT TENSIONER MAY NOT BE WORKING LIKE IT SHOULD.
ALSO, THE BATTERY MAY BE GOING DEAD WHILE YOU ARE PARKED. WHEN YOU RESTART, THERE IS A VERY LARGE LOAD ON THE ALTERNATOR AS IT TRYS TO RECHARGE THE BATTERY. CHECK BATTERY AFTER IS SITS OVER NIGHT.]
ROBERT

I had problems with my remote button, with battery fully charged turn on key for ten second, turn key off un-hook positve side of battery, re conect turn key to on postion then try to start, it worked for me I have a 2003 denali yukon XL, the motor would fire then stop.

Sounds like the alternator is going bad and killing the battery.