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Previous analyses of the large signal operation of optical parametric oscillators have considered uniform plane-wave pump beams. These analyses are not adequate to describe the behavior of efficient pulsed oscillators pumped by beams having nonuniform intensity profiles and pulse durations that are short enough that the steady-state transverse modes of the oscillator cavity do not become established. This situation is typical of oscillators with plane-parallel cavities pumped by -switched lasers. This paper theoretically and experimentally investigates the behavior of such oscillators when pumped with beams having Gaussian intensity profiles. Each of the three basic external optical parametric oscillators are considered. For simplified cases it is shown that the response to a Gaussian pump beam is quantitatively and qualitatively much different than that predicted by the uniform plane-wave calculations. Experimental results in fair agreement with these calculations are presented. More importantly, uniform plane-wave behavior was observed by using an aperture to probe a small section of the pump beam transmitted through the oscillator. This useful technique gives a sensitive indication of the oscillator operation and, at present, it is the most accurate means of measuring thresholds in pulsed oscillators. As a result of our calculations and experiments, previous experimental observations that were puzzling are now well understood.