The motions of relativistic particles in a magnetosonic shock wave propa- gating obliquely to an external magnetic field are studied. In the zeroth-order theory, particles continue to move nearly parallel to the external magnetic field in the shock transition region, when the shock speed is close to $c \cos \theta$, where $c$ is the speed of light and $\theta$ is the propagation angle. Perturbations to this zeroth-order motion are also analyzed for positrons and ions. The perturbation frequency of positrons is $\omega \sim \Omega_{\rm p0} \gamma^{-1}$ and that of ions is $\omega \sim \Omega_{\rm i0} \gamma^{-1/2}$, where $\Omega_{\rm p0}$ and $\Omega_{\rm i0}$ are the non-relativistic gyrofrequencies of positrons and of ions, respectively, and $\gamma$ is the Lorentz factor. These theoretical predictions are confirmed with numerical simulations.