We discuss the role that group-velocity dispersion and cavity detuning play in the onset of mode locking in synchronously pumped optical parametric oscillators. Because of the phase-sensitive character of the parametric gain, it is shown for the degenerate case that dispersion effects associated with off-resonance operation can lead to subpulse structures and spectral splitting of the parametric pulses. This behavior is interpreted on the basis of a dispersion-induced interference phenomenon between the two nearly degenerate parametric photons produced by the conversion of one pump photon in the nonlinear medium.