We describe a radiative transfer method for treating nongray gaseous absorption and thermal emission in vertically inhomogeneous multiple scattering atmospheres. We derive probability density distributions of absorption coefficient strength from line-by-line calculations to construct line-by-line and band model based k distributions. The monotonic ordering of absorption coefficient strengths in these k distributions implicitly preserves the monochromatic structure of the atmosphere at different pressure levels, thus simulating monochromatic spectral integration at a fraction of the line-by-line computing cost. The k distribution approach also permits accurate modeling of overlapping absorption by different atmospheric gases and accurate treatment of nongray absorption in multiple scattering media. To help verify the accuracy of the correlated k distribution method, we compare radiative cooling rates by atmospheric water vapor, CO2, and ozone against line-by-line calculations. The results show the correlated k distribution method is capable of achieving numerical accuracy to within 1% of cooling rates obtained with line-by-line calculations throughout the troposphere and most of the stratosphere.