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This paper is a theoretical examination of the frequency instabilities of the doubly resonant parametric oscillator. Such instabilities, caused by attempts to resonate simultaneously fields of two frequencies in unstabilized dispersive optical cavities, largely account for the poor performance of early parametric oscillators. The effects of reducing the of one of the resonant cavities of the doubly resonant oscillator are treated in detail. An analysis is given that predicts the frequency instabilities resulting from the presence of a slight feedback at the nonresonant mode in a nearly singly resonant oscillator. The analysis shows that the nonresonant mode feedback must be completely eliminated to prevent double-cavity oscillator-frequency instabilities.