Abstract: Based on the contact equivalent elation of smooth map-germs in singularity theory, the stability of quivariant bifurcation problems with two types of state variables nd their unfoldings in the presence of parameter symmetry is iscussed. Some basic results are obtained. Transversality condition s used to characterize the stability of equavariant bifurcation roblems.

Key words: equivariant bifurcation problem, unfolding, k-stability, k-infinitesimal stability