The ''reduced'' system of equations commonly used to describe the time evolution of the polar wind and multiconstituent stellar winds is derived from the equations for a multispecies plasma with known temperature profiles by assuming that the electron thermal speed approaches infinity. The reduced system is proved to have unbounded growth near the sonic point of the protons for many of the standard parameter cases. For the same parameter cases, however, the unmodified system (from which the reduced system is derived) exhibits growth in some of the Fourier modes, but this growth is bounded. (A physical explanation is provided for the unbounded growth in the reduced system and the bounded growth in the unmodified system.) An alternate system (the ''approximate'' system) in which the electron thermal speed is slowed down is introduced. The approximate system retains the mathematical behavior of the unmodified system and can be shown to accurately describe the smooth solutions of the unmodified system. The approximate system has a number of other advantages over the reduced system. For example, when the proton speed approaches the electron sound speed, the reduced system becomes inaccurate. Also, for three-dimensional flows the correct reduced system requires the solution of an elliptic equation, while the approximate system is hyperbolic and only requires a time step approximately 1 order of magnitude less than the reduced system. Numerical solutions from models based on the two systems are compared with each other to illustrate these points. ¿ American Geophysical Union 1992