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Summary form only given. When an optical parametric oscillator (OPO) is above threshold, the oscillator frequencies of the signal and idler modes are determined by the phase-matching condition, which is satisfied in a rather broad frequency range, and by the resonances of the cavity, which change with the cavity length. Consequently, in OPOs, the exact oscillation frequencies cannot be controlled very precisely, which can be a serious drawback. For example, the regime in which the signal and idler modes have exactly the same frequency, equal to half the pump frequency, is obviously very important to reach in metrology, but also in quantum optics where degenerate OPOs have many interesting quantum properties. Recently, Mason and Wong (1998) demonstrated experimentally that one can force the signal and idler modes of an OPO to oscillate at the same frequency by inserting a quarter-wave plate inside the OPO cavity that contains a type II phase-matched nonlinear crystal (with orthogonally polarized signal and idler). The aim of this presentation is to give a detailed theoretical analysis of this phenomenon.