This paper uses cones of topological vector spaces in place of cones of Banach spaces to investigate relations on TVS-cone metric spaces. It is proved that if $f$ is a compact-valued continuous relation on a TVS-cone metric space $X$, then $f^n$ is a compact-valued continuous relation on $X$ for each $n \in \Bbb N$. This result generalizes domains of compact-valued continuous relations from metric spaces to TVS-cone metric spaces, and improves a result for compact-valued continuous relations by omitting "locally compactness" of domains.