  Let $H_1$ and $H_2$ be two Hilbert spaces, $K$ and $L$ be bounded operatrors
on $H_1$ and $H_2$ respectively. In this paper we study the relationship
between $K$-frames for $H_1$ and $L$-frames for $H_2$ and $K\oplus L$-frames
for $H_1\oplus H_2$. The $K\oplus L$-minimal frames and $K\oplus L$-orthonormal
bases for $H_1\oplus H_2$ are also studied.
