The evolution of the electron velocity distribution function (VDF) in high-speed solar wind streams is modeled taking the expanding geometry, the polarization electric field, and Coulomb collisions into account. The VDF we find at the orbit of Mercury is composed of an isotropic, collision-dominated core, a trapped, anisotropic population called halo in this study, and a narrow, high-energy strahl that escapes along the magnetic field. The distribution function is very similar to the electron VDF observed in the low-density, high-speed solar wind by Pilipp et al. [1987> and Phillips et al. [1989>. The main features of the VDF can be obtained by considering only electron self-collisions; the effect of proton collisions is to make the distribution function more isotropic. At low energies, collisions with protons dominate the angular scattering, but electron self-collisions alone are frequent enough to keep the core of the distribution function quite isotropic. The expanding geometry produces an anisotropic halo and a narrow strahl. The angular scattering by protons reduces the anisotropy of the trapped halo particles and broadens the lower-energy part of the strahl. Along the magnetic field the resulting electron velocity distribution is composed of a relatively cold core and a halo-strahl spectrum that is flatter than the coronal spectrum. The two-temperature electron distribution function often observed in the solar wind may therefore be produced by Coulomb collisions and should not be taken as a proof of a non-Maxwellian (two-temperature) distribution function in the corona. ¿ 2000 American Geophysical Union