The propagation of relativistic electrons through the magnetosheath and solar wind is investigated in the two extremes of scatter-free motion and diffusive motion. For a source which is assumed on a field line close to the magnetopause, predictions are made of density U (or omnidirectional intensity) and anisotropy &xgr; at differential points on the field line in the magnetosheath and upstream solar wind. Both extremes of motion predict in the solar win thed a lower U than in magnetosheath. However, while scatter-free motion always gives greater anisotropy in the solar wind, in the diffusion case it depends on the locations of the comparison stations. The theory has been applied to observations >200 keV electrons, and derived mean free paths in the magnetosheath are 3.8¿0.6 RE and 8.7¿0.6 RE on two separate transversals, while the average results over a 4-year period give ≈1.0 RE. The latter value agrees with &lgr; = 1 RE obtained by an independent analysis of the same data set. The mean free path has also been computed from quasi-linear theory and measured magnetic power spectra. These give &lgr; varying from 0.27 RE for a typical high to 4.6 RE for a typical low level of disturbance in the magnetosheath, respectively. A particularly 'quiet' period gave &lgr; = 42.7 RE. The emperical results of &lgr; = 3.8 and 8.7 RE, obtained when KP≈2, are consistent with the low level of disturbance, while the average result of &lgr;≈1.0RE lies right between the low and the high.