[en] Earlier Sagdeev pseudopotential treatments of ion-acoustic double layers in plasmas with two electron populations were based on a model in which both electron densities were described by isothermal Boltzmann distributions. Using a more recent fluid-dynamical approach, with polytropic equations of state indices gamma(j), one finds analytically that no double layers can be formed for gamma(j)>= 3/2, due to total rarefaction of the cooler electrons or infinite compression of the ions. For gamma(j)< 3/2, rarefactive double layers occur, but, just below 3/2, at unrealistically small cool electron densities or large Mach numbers. As gamma(j) decreases towards 1, these constraints become less restrictive and go over smoothly to those known from Boltzmann studies. Contrary to what appears in the literature, very weak compressive double layers can also be found for Boltzmann electrons, but only for soliton conditions barely above the existence threshold; i.e., marginally super-ion-acoustic. Any slight increase in the critical Mach number destroys the possibility of having positive double layers, and, within the limits of numerical accuracy, no window could be found for gamma(j)not equal 1, where compressive double layers exist.(c) 2006 American Institute of Physics.