I have an APC Back-UPS ES.
I have a Dell laptop running Win2k and a desktop running RedHat 9 plugged in to it.
When power goes out, the laptop keeps running, but the desktop loses power.
Is this a linux issue?

No. Could it be that the reason the laptop keeps running is because it switches to using battery power? In any case if you want to test your UPS, I'd say the best way to do it is to plug lamps into it, then kill the power to see what happens (I would not recommend using expensive computer equipment to test a UPS). Obviously, if the lamps stay on, the UPS is good, if not, then either the battery needs charging, or it's defective in some way. Note that some power units are designed so that if power is lost, the switch will stay off until manually turned on. This is actually a good safety feature, because if the power supply is unstable for a while, you wouldn't want to have your machine have to ride out a series of surges. The "go down and stay down" design is intended to deal with that. -- J.W.

Probably not...
Read the manaul and the back of the UPS. There are usually two different types of outlets.
1. Controlled by UPS
2. Surge suppressed but not connected to UPS.

Do you have the interface cable connected to either PC?

JW, Good idea to check the laptop battery, I didn't think of that. But this is not the problem.
Also thanks for the recommendation to not use my computers for power testing purposes,
Instead i used my handy circuit tester, with which I discovered, as michaelk suggested,
that some of the sockets are surge protect only. The laptop was connected to a UPS socket
and the desktop to a surge protect only socket. Guess I should have rtfm.
Thanks.