Internal protein dynamics is essential for biological function. During evolution, protein divergence is functionally constrained: properties more relevant for function vary more slowly than less important properties. Thus, if protein dynamics is relevant for function, it should be evolutionary conserved. In contrast with the well-studied evolution of protein structure, the evolutionary divergence of protein dynamics has not been addressed systematically before, apart from a few case studies. X-Ray diffraction analysis gives information not only on protein structure but also on B-factors, which characterize the flexibility that results from protein dynamics. Here we study the evolutionary divergence of protein backbone dynamics by comparing the C(alpha) flexibility (B-factor) profiles for a large dataset of homologous proteins classified into families and superfamilies. We show that C(alpha) flexibility profiles diverge slowly, so that they are conserved at family and superfamily levels, even for pairs of proteins with nonsignificant sequence similarity. We also analyze and discuss the correlations among the divergences of flexibility, sequence, and structure.