A model of the magnetopause current layer is constructed on the basis of fluid equations for collision-free plasmas with finite ion Larmor radius (FLR). The model provides self-consistent solutions for the plasma flow vector, magnetic field, and electric currents inside the magnetopause layer. This is the first fluid model that offers explanations for some observations at the terrestrial magnetopause that are inexplicable by earlier models. In particular, it is shown that the erosion of the dayside magnetosphere can be explained by the normal component of the gyroviscous stress tensor that is related to the intensity of field-aligned currents inside the magnetopause layer. It is found that the sense of rotation of the magnetic field across the magnetopause is determined by the ratio of the normal component of the Alfv¿n velocity to the normal flow velocity &xgr;=Bn/(&mgr;0&rgr;)1/2Vn. For ‖ &xgr; ‖>1 the sense of rotation corresponds to electron polarization, and ‖ &xgr; ‖<1 yields proton polarization. It is argued that the case ‖ &xgr; ‖=1 corresponds to the formation of transient flux transfer events. The observed departures from MHD jump conditions across the magnetopause are explained by additional, finite Larmor radius terms in the moment equations. An expression is also derived for the characteristic thickness of the magnetopause layer. ¿ American Geophysical Union 1989