  We prove that if $\{\phi_t\}_{t \geq 0}$ is a CP-semigroup acting on a von
Neumann algebra $M \subseteq B(H)$, then for every $A\in M$ and $\xi \in H$,
the map $t \mapsto \phi_t(A)\xi$ is norm-continuous. We discuss the
implications of this fact to the existence of dilations of CP-semigroups to
semigroups of endomorphisms.
