Abstract: By applying coincidence theorems in part (Ⅰ) for two families of set-valued mappings defined on product space of noncompact FC-spaces in preceding paper, some new existence theorems for system of vector equilibrium problems, system of inequalities and system of minimax theorems were established in FC-spaces. These results generalize some known results in recent literature.

Key words: system of vector equilibrium problems, system of minimax inequalities, transfer compact upper (lower)semicontinuous, FC-space, FC-quasiconvex