Observations show that the solar wind ram pressure has large-scale fluctuations on the timescale of days to years. Such fluctuations will cause inward and outward motions of the heliospheric boundary, including the termination shock and the heliopause. A two-dimensional time-dependent hydrodynamic model for the interaction of the solar wind with the local interstellar medium, which includes the mutual interaction of the interstellar and solar wind plasma and the interstellar neutral hydrogen, is employed to study the changes in the global heliosphere brought about by both long-term (for example, 11-year solar cycle) and short-term (for example, tens of days) variations in the solar wind. The inclusion of neutrals is found to reduce the amplitude of the boundary motion. The size of the excursions of the termination shock in response to the 11-year solar cycle variation is about 13 AU per solar cycle in our calculation. The motion of the termination shock is asymmetric in time, that is, the termination shock moves outward faster than it moves inward, even though the 11-year variation is applied as a sinusoidal change at the inner boundary. The concurrent excursions of the heliopause are found to be much smaller than those of the termination shock, and the heliospheric bow shock seems unaffected by the solar cycle pressure variations. The motion of the termination shock due to shorter period (180 days) fluctuations in the solar wind is much smaller (3 to 4 AU), and the heliopause has little response to such short-term fluctuations. Possible crossing of the termination shock and the heliopause by the Voyager 1 spacecraft are discussed. ¿ 1999 American Geophysical Union