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A uniform plane-wave theory of the type previously employed for the optical parametric oscillator (OPO) is extended to include internal upconversion and frequency doubling. All the experimental configurations for internal upconversion and doubling in the three basic OPO types are treated. Generated intensities are calculated for representative system parameters, and both design parameters and quantum upconversion and doubling efficiencies are obtained for optimum operation in each configuration. The position of the upconverter in the OPO cavity relative to the oscillator crystal and input-pump direction is shown to affect efficiency and output characteristics drastically. The detrimental effects of internal up-conversion on threshold are shown to be an important design consideration. Applicability of the results to pulsed OPO internal upconversion and frequency doubling is determined, and design criteria for selecting the best mode of operation are discussed.