Measurements of the electron distribution function in the ion foreshock, by Active Magnetospheric Particle Tracer Explorers United Kingdom Subsatellite (AMPTE UKS), reveal distributions which vary on a ULF wave timescale between anisotropic (Te∥>Te⊥) and approximately isotropic (Te∥≈Te⊥). The electron anisotropy changes quasi-periodically in reasonable correlation with the changes in the magnetic field magnitude, so that high field regions coincide with the more isotropic distributions. Individual contours of phase space density display these correlations over a large region of velocity space. By mapping these contours through several wave cycles, we show that such changes in anisotropy can be largely explained by the conservation of the magnetic moment and energy of the electrons moving through different magnetic field regions. The wave electrostatic potential can also be inferred from Liouville mapping of the thermal electron distribution functions. The time-averaged electron distribution is hotter than it would be in the absence of the ULF wave field, but this is due to the adiabatic behaviour of the electrons, rather than to irreversible scattering. ¿ American Geophysical Union 1996