Can I bi-amp my speakers with two different amps?

Do note that biamp arrangements can also hurt speaker coherence. I biamp my Coincident PRE's, but getting levels/frequencies properly balanced is a real challenge.  I probably should have invested in a quality microphone and done some real measurements to help with set-up. 

george and eric hit the important points - selecting the right amp for each and equalizing the gains.

Of course this is very obvious, but be sure to remove the "shorting straps" prior to bi-amping or bi-wiring for that matter.  

@68pete
Did you really have to type your last sentence?? hehehe

It would be interesting jokomo to share what it does to enhance your overall sound.

Just to save you from blowing something up, be sure the amps are not connected to a common ground at the speaker end. Remove any connection at the speaker that ties the woofer and tweeter terminals together in ANY way. Keep them totally separate. To feed the amps the same signal, just use one of those "Y" connectors that give you two female phono sockets and one phono plug.