GTPases constitute a superclass of proteins with a common fold. Five specific G motifs located in loops are signatures of this superclass. Nevertheless, some proteins may share the fold of the small GTPases, although their functions are totally unrelated. To retrieve them, we specifically searched in the BLAST output listings for non-GTPases with available 3D structure, starting from a canonical GTPase sequence as a query. We then performed both a sequence analysis by means of HCA and a structural comparison with an established GTPase. It results that, although sequence identity is in the twilight zone, i.e. below 25%, one can evidence some conservations of the catalytic motifs. Nevertheless, mutations have occurred that produced a new function while the global fold is maintained. We discuss whether non-GTPases presumably originated from a common ancestor with an ancient G domain. The evolutionary mechanisms relating non-GTPases to GTPases that we can advance are sequence divergence, convergence, and DNA recombination. We conclude that the most probable evolutionary pathway leading to such structural similarities is that all the studied proteins must have evolved by sequence divergence from a primordial GTP-binding domain.