In this study, we evaluated the ability of Mapping Neural Networks (MNNs) to calculate the high-resolution radiant fluxes of one-dimensional and two-dimensional inhomogeneous clouds. The tests were done for different types of clouds, radiant fluxes, and wavelengths under different conditions of illumination. The MNNs were trained with training data sets composed of the Monte Carlo (MC) radiant fluxes of bounded cascade clouds and used to compute first the high-resolution MC radiant fluxes (reflectance, transmittance, and absorptance) of bounded cascade inhomogeneous clouds. The tests showed their rather good performance, which was compared with that of the Nonlocal Independent Pixel Approximation when possible. Their generalization ability was, second, tested with inhomogeneous clouds of other types: white noise clouds and bounded cascade inhomogeneous clouds with fractional cloud cover. In these cases, the MNNs, trained with different fields, have still good performance. However, the results were found to be much better for the reflectance than for the transmittance and absorptance. In the case of fractional cloud cover, debased responses appear as well in transition zones. We show that the generalization ability could be improved significantly by completing the training sets with new additional patterns when they are applied to types of inhomogeneous clouds different than the clouds of the training set. These results reveal that the MNNs represent a flexible method of function approximation to compute the high-resolution radiant flux of bounded cascade and other inhomogeneous clouds. ¿ 2001 American Geophysical Union