The structure of the low-latitude magnetopause is investigated for interplanetary magnetic field conditions with a dominant southward component using magnetohydrodynamic simulations. The structure is self-consistently calculated as an initial-value problem in which the system is allowed to evolve to a quasi steady state. All components of the three-dimensional velocity and magnetic field as well as compressibility, resistivity, and viscosity are included in the two-dimensional calculation. The boundary conditions sustain inflow from the magnetosheath and the magnetosphere, as well as a flow tangential to the magnetopause, sunward in the magnetosphere and tailward in the magnetosheath. The tangential flow leads to the draping of magnetic field lines in the magnetopause region. No draping (tailward or sunward) was included initially, while as the system evolved this component of the magnetic field became comparable in magnitude to the other two components. The resulting draping structure is found to be dependent sensitively on the ratio of the viscous and magnetic diffusivities. ¿American Geophysical Union 1991