The strahl component of solar wind electrons, which constitutes field-aligned electron heat flux running away from the Sun, is a strong candidate for the origin of the polar rain. We investigate the entry process of the strahl electrons into the distant-tail magnetosphere and discuss topologies of Earth's field lines in this paper. The Geotail satellite has often observed either gradual or abrupt transitions from the magnetosheath electrons to the bidirectional lobe electrons at the magnetopause. In some cases, the strahl flux of the sheath electrons flowing tailward gradually turned near the magnetopause and finally became the earthward flux of the bidirectional lobe electrons. This transition is accompanied by the rotation of the magnetic field direction and indicates the direct entry of the strahl electrons along open field lines. On the basis of the data of 38 magnetopause crossings by Geotail, we investigate variation of density of the strahl (polar rain) electrons and that of ion density near the magnetopause. It is shown that the strahl electrons decrease upon crossing the magnetopause, and the decrease is correlated with that of ions, although, quantitatively, the strahl electrons do not decrease so much as ions. It is suggested that the strahl electrons enter the magnetosphere along open field lines more freely than ions, but their entry is under the influence of charge neutrality with ions. It remains as a problem why the Geotail data do not show the presence of electrons escaping from the magnetosphere along open field lines. ¿ 1998 American Geophysical Union