- A class of mean annual zonally averaged energy-balance climate models of the Budyko-Sellers type are studied by a spectral (expansion in Legendre polynomials) method. Models with constant thermal diffusion coefficient can be solved exactly. The solution is approached by a rapidly converging sequence with each succeeding approximant taking into account information from ever smaller space and time scales. The first two modes represent a good approximation to the exact solution as well as to the present climate. The two-mode approximation to a number of more general models are shown to be either formally or approximately equivalent to the same truncation in the constant diffusion case. Details of the dynamics do not influence the first two modes. Estimated ice age temperatures and ice line latitude agree with the model if the solar constant is reduced by 1. 3%.