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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 onlyone non-zero coupling at a time, the process $e^+e^-\to W^+ W^-$ can be used toplace 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. Bystudying certain distributions in the process $e^+e^-\to\mu^+\mu^-\nu\bar{\nu}$ one of the bounds can be improved to $|g_4^Z| \leq0.06$. This process also allows the construction of a CP odd observable whichcan be used to place bounds on CP violating new physics. At the 95% confidencelevel we find $|\tilde\kappa_\gamma|\leq 0.3$, $|\tilde\kappa_Z|\leq 0.2$ and amuch weaker bound for $|g_4^Z|$.Comment: 18 pages LaTeX, 11 figures using eps

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>CP</mml:mi></mml:math>violating anomalous couplings at a<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>500</mml:mn><mml:mi /><mml:mi mathvariant="normal">GeV</mml:mi></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow><mml:mrow><…

CPviolating anomalous couplings at a500GeVe+<…