  We study the sensitivity of a 500 GeV $e^+e^-$ Linear Collider to $CP$
violating anomalous couplings. We find that with 50~fb$^{-1}$, and taking only
one non-zero coupling at a time, the process $e^+e^-\to W^+ W^-$ can be used to
place the 95% confidence level bounds $|\tilde\kappa_\gamma|\leq0.1$,
$|\tilde\kappa_Z|\leq 0.1$ and $|g_4^Z|\leq 0.1$ from CP even observables. By
studying certain distributions in the process $e^+e^-\to
\mu^+\mu^-\nu\bar{\nu}$ one of the bounds can be improved to $|g_4^Z| \leq
0.06$. This process also allows the construction of a CP odd observable which
can be used to place bounds on CP violating new physics. At the 95% confidence
level we find $|\tilde\kappa_\gamma|\leq 0.3$, $|\tilde\kappa_Z|\leq 0.2$ and a
much weaker bound for $|g_4^Z|$.
