The singular points in steady state, field-aligned plasma transport models based on velocity moment theory are examined. In particular, two separate singular points in the equations obtained from the 16-moment approximation are identified. These equations are presented in a form that makes the singularities apparent, and they are solved in a simple illustrative case. The singular points, one occurring at the sonic point and the other at a critical value of the parallel heat flux, give rise to different outflow regimes, characterized generically by different assymptotic behavior. The existence of the different outflow regimes separated by the heat flux critical point has been only hinted at in previous discussions of numerical simulation of the polar wind. ¿American Geophysical Union 1990