We report the theoretical analysis of a simultaneously phase-matched tandem optical parametric oscillator (STOPO) in which the principal OPO generates a signal which pumps a secondary OPO. Both OPO interactions are assumed to be phase-matched in a single crystal. The cavity has high Q for the signal produced by the principal OPO and has lower Q for the signal of the secondary OPO. The pump and the two idler frequencies are not resonated. The five waves undergoing nonlinear mixing are assumed to be nondegenerate in either frequency or polarization. We show that the useful output, consisting of the two idlers and the signal of the secondary OPO, can be produced with high efficiency over a large dynamic range in the pump intensity. We discuss the tuning with temperature and grating period of a STOPO based on periodically poled LiNbO/sub 3/ pumped at 1.064 /spl mu/m. We present results based on both plane-wave modeling and modeling in three spatial dimensions.