In this paper, we frst introduce the notion of strong quasiconvexity of a vector-valued map. Then, this new condition is utilized to study the existence and stability of solutions to parametric vector Ky Fan inequalities. Namely, sufcient conditions for the nonemptiness of solutions and the Hölder continuity of solution maps to parametric vector Ky Fan inequalities are established. The results obtained in this paper are improvements of the previous ones. At the end of the paper, applications of the main results are presented.