A general formulation is given of the multi-level rotation vibrational non-LTE problem for a mixture of radiating molecular gases in a planetary atmosphere, treating explicitly the coupling of molecular energy levels by collisionally induced energy transfer processes and by band overlap. Various limiting cases of non-LTE effects are discussed. Three techniques - lambda iteration, matrix and accelerated lambda iteration - which are used to solve these problem are discussed and compared. In the case of the CO₂ non-LTE problem in the Earth's atmosphere, it is demonstrated that accelerated lambda iteration is far superior to the other algorithms in minimizing computer time and storage and in converging much more rapidly; moreover the convergence rate is insensitive to the initial population estimates and to wide range of variation in the model input parameters. Accelerated lambda iteration therefore makes possible the calculation of much larger and more physically complete atmospheric and molecular models.