We theoretically investigate the generation of spatial patterns in intracavity second-harmonic generation. We consider a cavity with planar mirrors that is resonant at the fundamental frequency, but not at the second-harmonic frequency. A mean-field model is derived that describes the resonant fundamental field, and its coupling to a pair of nondegenerate parametric fields. The parametric fields are driven by the nonresonant second-harmonic field. Analysis indicates the existence of transverse instability of the pump field alone, as well as the possibility of simultaneous instability of the pump and the parametric fields. A range of spatial structures including periodic planforms as well as spatially localized states are found numerically. The simplicity of the singly resonant cavity makes it well suited for experimental studies. Estimates of experimental parameters necessary for observation of spatial structures are given. [S1050-2947(99)02810-3].