A sequence of steady, oblique, C-type shock waves differing in the angle between the ambient magnetic field and the direction of shock propagation, θS, are examined for stability to small perturbations in the plane containing the fluid velocities and the magnetic field. As θS is reduced the steady shocks become stronger and the growth rate and wavenumber of the fastest growing mode increase. The growing perturbations propagate across the face of the shock front at a speed of order the Alfven speed in the pre-shock gas (typically 2 km s-1 in molecular clouds). The strength of the density perturbations in the neutral gas decreases relative to those in the ions as θs is reduced, and the perturbations in the neutral gas resemble ripples rather than the clumps found in the perpendicular case. It is noted that a similar instability may arise in other situations in which ambipolar diffusion plays a major role.