The issue of whether a shock forms in the interstellar medium as it approaches the heliopause has not been settled. Observations generally show that the local interstellar medium is slightly supersonic with respect to a stationary (constant distance from the Sun) heliopause. The solar wind dynamic pressure varies over the solar cycle, causing the heliopause distance to move inward and outward. This work shows that the heliopause speeds may be large compared to the speed of the interstellar medium. This leads to the scenario where the interstellar medium is supersonic with respect to the heliopause when the heliopause moves outward (the declining phase of the solar cycle) and subsonic the rest of the time. A shock would form when the heliopause moves outwards and dissipate when the heliopause moves inwards. The heliospheric radio emission is shown to occur at times when the heliopause moves outwards and thus may be related to the formation of the shock in the interstellar medium. This work leads to two testable predictions: 1) that the heliospheric radio emissions will intensify when the solar wind pressure increases and 2) the temperature of the interstellar neutrals will fluctuate over a solar cycle with larger temperatures when there is a shock in the interstellar medium. ¿ 1997 American Geophysical Union