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Summary form only given. We find that, as the system is pumped above optical parametric oscillator (OPO) threshold, the intracavity singly resonant optical parametric oscillator (ICSRO) dynamics diverge rapidly from those of the basic Nd:YVO/sub 4/ laser. In particular, damping times become much longer than those of the laser transients. While amplitude fluctuations will always be damped away (in contrast to the Green problem), the ICSRO is slower in responding to a perturbation, and so is more susceptible to relaxation oscillations, than the basic laser. The practical implications of these results to Nd:YVO/sub 4/ based ICSROS will be discussed.