The results of a three-dimensional adaptive magnetohydrodynamic (MHD) model of the interaction of a magnetized solar wind with a magnetized very local interstellar medium in the presence of neutral interstellar hydrogen are presented. The interplanetary magnetic field is approximated by the Parker spiral, and the direction of the interstellar magnetic field is taken to be arbitrary. It is demonstrated that magnetic field interaction has a very pronounced effect on the structure of the global heliosphere. In particular, it is shown that the interaction of the interstellar wind with the shocked solar wind significantly depends on the direction of the interstellar magnetic field. This effect is mainly manifested in the distances to the heliospheric boundaries and the shape of the heliosphere. Depending on the orientation of the interstellar magnetic field the upstream location of the termination shock is expected to be at 80¿10 AU. The termination shock is predicted to be weak in agreement with the available body of observations. It is found that under quiet solar conditions the spiral structure of the interplanetary magnetic field remains imprinted in the solar wind far beyond the termination shock. Numerical simulations indicate that magnetic fields have a stabilizing effect on the heliopause. ¿ 1998 American Geophysical Union