Up-to-date approaches to modeling the climate and tendencies of its changes are considered, their merits and demerits are analyzed, and main difficulties arising in solution of the modeling problems are pointed out. An approach is proposed to estimate climate change tendencies; it is based on the use of ideas and methods of the sensitivity theory of distributed systems. New methods of the sensitivity theory are developed, and models of sensitivity of climatic models to variations of their parameters are constructed. The equations for the functional sensitivity depending on solution of the equations of fluid-dynamics models are derived.