Rapid rates of evolution can signify either a lack of selective constraint and the consequent accumulation of neutral alleles, or positive Darwinian selection driving the fixation of advantageous alleles. Based on a comparison of 1,350 orthologous gene pairs from human and mouse, we show that the evolution of gene expression profiles is so rapid that it is comparable to that of paralogous gene pairs or randomly paired genes. The expression divergence in the entire set of orthologous pairs neither strongly correlates with sequence divergence, nor focuses in any particular tissue. Moreover, comparing tissue expressions across the orthologous gene pairs, we observe that any human tissue is more similar to any other human tissue examined than to its corresponding mouse tissue. Collectively, these results indicate that, while some differences in expression profiles may be due to adaptive evolution, the levels of divergence are mostly compatible with a neutral mode of evolution, in which a mutation for ectopic expression may rise to fixation by random drift without significantly affecting the fitness. A disturbing corollary of these findings is that knowledge of where the gene is expressed may not carry information about its function.