The present paper studies some properties of c-K-g-frames in separable Hilbert spaces, which are extensions of K-g-frames and c-g-frames. In addition, necessary and sucient conditions for constructing c-K-g-frames are given by using bounded operators. The notion of c-K-g-duals for c-K-g-frames are introduced and such duals are charac- terized. Moreover, we also discuss on operators preserving c-K-g-frames. Finally, some equalities and inequalities about c-K-g-frames are investigated.
