  Gavruta introduced $K$-frames for Hilbert spaces to study atomic systems with
respect to a bounded linear operator. There are many differences between
K-frames and standard frames, so we study weaving properties of K-frames. Two
frames $\{\phi_{i}\}_{i \in I}$ and $\{\psi_{i}\}_{i \in I}$ for a separable
Hilbert space $\mathcal{H}$ are woven if there are positive constants $A \leq
B$ such that for every subset $\sigma \subset I$, the family $\{\phi_{i}\}_{i
\in \sigma} \cup \{\psi_{i}\}_{i \in \sigma^{c}}$ is a frame for $\mathcal{H}$
with frame bounds $A, B$. In this paper, we present necessary and sufficient
conditions for weaving $K$-frames in Hilbert spaces. It is shown that woven
$K$-frames and weakly woven $K$-frames are equivalent. Finally, sufficient
conditions for Paley-Wiener type perturbation of weaving $K$-frames are given.
