A topological space $\left(X,\tau \right)$ is called a $KC$-space when every compact subset of $X$ is closed. The aim of this paper is to introduce new, namely $KC$-bitopological spaces and pairwise $KC$-topological spaces " $P$- $KC$-topological spaces". We examined the properties of these concepts and showed the relationships between these concepts and other bitopological spaces. We also discussed the effect of some types of functions on $KC$-bitopological spaces and pairwise $KC$-topological spaces. Several examples are discussed, and many well-known theories are generalized.