Non-gray model atmospheres have been constructed for the major planets assuming and introducing first-order radiative-equilibrium corrections to account for convection. The thermal opacity was provided by the pressure-induced absorption of HI and also by its enhancement resulting from mixing with He The thermal opacity due to NH3 was found to be negligible in all of the major planets except Jupiter, where the effect is but minor. In constructing the models, the He/H abundance ratios and effective temperatures were considered free parameters to be determined by fitting the models to the observations. In all the models the absorption is strong enough to bring about convection in the deeper layers. In the case of the Jovian models, the amount of HI lying above the convective zone is found to be approximately equal to the observed amount lying above the planet's visual cloud layer. The Jovian limb darkening in the 8-14- region can be explained in terms of absorption due to 113, He, and the 10-i# band of NH1 but cannot be explained when the NH3 band is excluded. Models of Jupiter for which only the thermal opacity of HI and NH3 are taken into account are incompatible with the observations. Adding He, however, eliminates this incompatibility, indicating that He is present in these atmospheres. In the case of Jupiter, a rather large He/H value is implied if there is no internal heat source. However, the observations suggest that the value of He/H is less than 2 so that the existence of a small internal heat source generating more than one-tenth of the incident solar flux is implied.