In this paper we examine the stability of a steady solar wind dissipatively heated by Alfv¿n waves whose relative amplitude is saturated at a given level by nonlinear processes. It is shown that long-wavelength compressional modes can be driven unstable by dissipative heating arising from short-wavelength saturated Alfv¿n waves. Analytic expressions are derived for the marginal stability condition and the growth rates in the unstable region for the case of a moderate to low &bgr; plasma. These are supplemented by a numerical solution of the full MHD dispersion equation, including dissipative Alfv¿nic effects, which confirms the approximate analysis. It is shown that the growth time of the instability can be of the order of 7 times the characteristic period of an Alfv¿n wave for a wide range of parameters appropriate to the solar wind. The implication is that the compressional instability driven by dissipative Alfv¿n waves could play a significant role in the large-scale heating and dynamics of the solar wind, particularly in the supersonic region. ¿American Geophysical Union 1991