I have calculated AIC and AICc to compare two general linear mixed models; The AICs are positive with model 1 having a lower AIC than model 2.  However, the values for AICc are both negative (model 1 is still < model 2).  Is it valid to use and compare negative AICc values? 
All that matters is the difference between two AIC (or, better, AICc) values, representing the fit to two models.  The actual value of the AIC (or AICc), and whether it is positive or negative, means nothing. If you simply changed the units the data are expressed in, the AIC (and AICc) would change dramatically. But the difference between the AIC of the two alternative models would not change at all.

Bottom line: Ignore the actual value of AIC (or AICc) and whether it is positive or negative. Ignore also the ratio of two AIC (or AICc) values. Pay attention only to the difference.
