In the outer region of the heliosphere (> 20 AU) the neutral gas density becomes larger than the solar wind plasma density, which is inversely proportional to the square of the heliocentric distance. Thus the neutral gas drag may play an important role in the evolution of dust grains in this region. The effect is similar to the plasma Poynting-Robertson effect; the neutral hydrogen gas exerts a drag force on the dust particles. However, the monodirectional velocity of the interstellar gas, connected with the inflow direction of the interstellar material, induces an effect which is very much different from that induced by the radial solar wind velocity. This causes an asymmetric force acting on the dust particles, which forces the eccentricity and semimajor axis to change rapidly. As an effect of that the lifetime of dust grains in the Edgeworth-Kuiper Belt is not determined by the electromagnetic or plasma Poynting-Robertson lifetime but by the drag of the neutral gas leading to lifetimes of the order of half a million years for a 10-&mgr;m-sized particle. ¿ 2000 American Geophysical Union