We present two-and-one-half-dimensional (212-D) hybrid numerical simulations of a small group of oblique Alfv¿n waves with linear polarization. These are the first simulations of nonplanar Alfv¿n waves which evolve to a nearly constant-B state (spherical polarization) with imbedded rotational discontinuities (RDs). Initially, B varies with position in the wave group, and we consider only cases where the Fourier components of B2 are entirely oblique to the background magnetic field B0. When propagating in different directions but with group speeds in the same direction along B0, Alfv¿n waves generally evolve nonplanar waveforms with nearly constant magnetic intensity B. In this waveform, the magnetic field vectors move on a sphere of radius B and have a spherical rather than arc polarization. Most Alfv¿nic fluctuations in the solar wind are spherically polarized. We also find analytical second-order solutions from the magnetohydrodynamic equations for linearly polarized Alfv¿n waves in 212-D and 3-D. For moderate-wave amplitudes (|ΔB|/B0≲0.5), these show that the second-order driven wave solution can only remove variations of B when the Fourier components of B2 are oblique to B0. Large-amplitude (|ΔB|/B0~1) waves also evolve to constant magnetic intensity, but higher-order terms produce imbedded RDs with properties similar to those seen in the solar wind. The RDs are steady, and their normals are oblique to B0. The transverse extent of the RDs is approximately of order of the average wavelength of the Alfv¿n waves, and the RDs are either locally planar or fully nonplanar. RDs can appear at less than twice per cycle in waveforms composed of two or more waves. If the magnetic fields are sampled along a single line through the simulation box, as a single spacecraft would observe Alfv¿nic fluctuations in the solar wind, the rate depends on the direction that the line takes through the box. We also suggest that all Alfv¿nic fluctuations are spherically polarized, and instances of arc-polarized fluctuations occur when spacecraft sample locally planar structures.¿ 1998 American Geophysical Union