Proteins that show similarity in their equilibrium dynamics can be aligned by identifying regions that undergo similar concerted movements. These movements are computed from protein native structures using coarse-grained elastic network models. We show the existence of common large-scale movements in enzymes selected from the main functional and structural classes. Alignment via dynamics does not require prior detection of sequence or structural correspondence. Indeed, a third of the statistically significant dynamics-based alignments involve enzymes that lack substantial global or local structural similarities. The analysis of specific residue-residue correspondences of these structurally dissimilar enzymes in some cases suggests a functional relationship of the detected common dynamic features. Including dynamics-based criteria in protein alignment thus provides a promising avenue for relating and grouping enzymes in terms of dynamic aspects that often, though not always, assist or accompany biological function.