We use a 1-D chemical diffusive model, in conjunction with the measured neutral atmospheric structure, to analyze the Voyager RSS electron density, n(e), profiles for the ionospheres of Jupiter and Saturn. As with previous studies we find serious difficulties in explaining the n(e) measurements. The model calculates ionospheres for both Jupiter and Saturn with n(e) peaks of approximately 10 times the measured peaks at altitude which are approximately 900 - 1000 km lower than the altitude of peaks in the RSS electron densities. Based on our knowledge of neutral atmospheric structure, ionization sources, and known recombination mechanisms it seems that, vibrational excitation of H-2 must play some role in the conversion of slowly radiatively recombining H+ ions to the relatively more rapidly recombining H-2+ and H-3+ ions. In addition, vertical ion flow induced by horizontal neutral winds or electric fields probably also play some role in maintaining the plasma peaks observed both for Jupiter and Saturn to be at high altitudes. For the ionosphere of Saturn, the electron densities are affected by a putative influx of H2O molecules, PHI(H2O), from the rings. To reproduce the RSS V2 exit n(e) results model requires an influx of PHI(H2O) approximately 2 x 10(7) molecules cm-2 S-1 without invoking H-2 vibrational excitation. To maintain the model n(e) peak at the measured altitude vertical plasma drift maintained by meridional winds or vertical electric fields is required. The amounts of H2O are consistent with earlier estimates of Connerney and Waite (1984) and do not violate any observational constraints.