A large variety of signal transduction processes involve bivalent attachment of protein ligands to molecular determinants on cell surfaces. In these processes, there may be significant dynamic conversion between dissociated, monovalently bound, and bivalently bound ligands. The possibility that these dynamics might occur to a substantial degree suggests that bivalent proteins might move laterally across cell surfaces by sequential detachment and attachment of single binding sites. It is the purpose of this work to theoretically define when this putative mode of translational mobility, called "walking", might occur. Two aspects of the physiological significance of this question are addressed : the average number of steps walked before dissociation, and the average translational diffusion coefficient arising from the walking mechanism. Both symmetric and asymmetric bivalent ligands are considered.