The interaction of dust grains originating from the local interstellar cloud with the environment inside the heliosphere is investigated. As a consequence of this interaction, the spatial distribution of interstellar dust grains changes with time. Since dust grains are charged in the interplanetary plasma and radiation environment, the interaction of small grains with the heliosphere is dominated by their coupling to the solar wind magnetic field. The change of the field polarity with the solar cycle imposes a temporal variation of the spatial distribution and the flux of small (radius smaller than 0.4 &mgr;m) interstellar dust grains in the solar system, whereas the flux of large grains is constant because of their negligible coupling to the solar wind magnetic field. The flux variation observed by in situ measurements of the Galileo and Ulysses spacecraft are reproduced by simulating the interaction of interstellar grains with charge-to-mass ratios between 0.5 and 1.4 C kg-1 with the interplanetary environment. ¿ 2000 American Geophysical Union