This chapter considers approximations of vector quasiequilibrium problems and their particular case: vector Nash quasigames (vector generalized noncooperative games), which are among the most important models in applied mathematics. Since there have been no studies of variational convergence of vector bifunctions in the literature, our approach consists of first scalarizing the problems by the Tammer and Hiriart-Urruty methods and then applying variational convergence of scalar bifunctions. Sufficient conditions for convergence of the three types of approximate solutions of the problems approximating the original one under appropriate types of variational convergence are established.