During periods of a persistent southward interplanetary magnetic field, reconnection is initiated at the dayside magnetopause and flux is transported away to the nightside magnetosphere. This is the so-called phenomenon of magnetosphere erosion. In this paper, erosion at the terrestrial magnetopause is studied. A new theoretical approach to study erosion at the magnetopause on the basis of time-dependent reconnection is presented. We calculate the earthward motion of the magnetopause resulting from each reconnection pulse, together with the associated bow shock motion. Thus, the displacement of both boundary layers is presented.