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We investigate the modulational instability in a nonlinear dispersive cavity which is driven to oscillation by degenerate parametric interaction in a nonlinear χ(2) medium. Our analysis predicts the existence of stable temporal dissipative structures mediated by modulational instability when oscillation occurs through a subcritical instability. Decreasing the parametric gain below the subcritical bifurcation point, stability of these structures is broken and complicated temporal patterns in the form of weakly interacting solitary waves are predicted. © 1995 American Institute of Physics.