The solution of the generalized two-stream approximation for radiative transfer in homogeneous multiple scattering atmospheres is extended to vertically inhomogeneous atmospheres in a manner which is numerically stable and computationally efficient. It is shown that solar energy deposition rates, photolysis rates, and infrared cooling rates all may be calculated with simple modifications of a single algorithm. The accuracy of the algorithm is generally better than 10% so that other uncertainties, such as in absorption coefficients, may often dominate the error in calculation of the quantities of interest to atmospheric studies. ¿ American Geophysical Union 1989