The transverse mode structure of a tapered-wiggler free-electron laser (FEL) oscillator operating at full saturated intensity is analyzed numerically. The unique features of the FEL geometry, and particularly the refractive property of the -beam, which acts like a series of small focusing lenses, tend to produce a steady-state mode structure different from the TEM00mode of the cavity. The higher order mode content is especially evident in confocal cavities, since higher order modes constructively interfere on different round trips. Constructive addition of higher-order modes is also expected in practical FEL's operating at substantial power levels using near-concentric cavities. The presence of higher order modes has unusual effects on the intracavity intensity distribution of a confocal cavity, including different spot sizes on the front and rear mirrors and different transverse structure on forward and reverse passes. Nevertheless, the output beam quality is nearly diffraction limited for the low gain, low Fresnel number cases studied. Noticeable higher order mode content is also expected for near-concentric cavities.