This paper presents a theoretical analysis of self-doubling optical parametric oscillators (OPO's) where a single nonlinear crystal is used for both parametric generation and frequency doubling. In these devices, the parametric generation and frequency-doubling processes are both phase matched for the same direction of propagation inside the crystal. Different polarization geometries for which this simultaneous phase-matching condition can potentially be satisfied are identified and categorized. Plane-wave coupled-mode equations are presented for each of these categories. Numerical solutions of these coupled-mode equations and calculation of the single-pass saturated signal gain are outlined. Intracavity signal photon flux calculations iased on these numerical solutions are presented. The dependence of performance measures such as the photon conversion efficiency on various design parameters are investigated.