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The reproduction of the current state of the Earth climate system with the help of a mathematical model is considered. The model has been developed at the Institute of Numerical Mathematics of the Russian Academy of Sciences (INM RAS). This model describes the following processes: general circulation of the atmosphere, general circulation of the ocean including the sea ice evolution, the transfer and chemical transformations of several tens of small gaseous components, and the carbonic and methane cycles.Climatic models are justifiably considered to be most powerful instruments for study of various mechanisms and feedbacks in a climatic system, and mathematical modelling of climate changes is considered the most reliable method for prediction of these changes. Such climatic models include two basic blocks: a model of global atmospheric circulation and a model of general circulation of the ocean. In addition, lately more and more models include interactive calculations of the carbonic cycle and atmospheric chemistry, because the feedback in the climate-carbonic cycle system or the climate and atmospheric chemistry system is essential and should be taken into account in prediction of probable climate changes. Models including all mentioned blocks are generally called the models of the Earth system. As a rule, models of the Earth system were developed in the course of many years, and initially all of the blocks, i.e., the dynamics of the atmosphere, the dynamics of the ocean, atmospheric chemistry, and the carbonic cycle, were simulated separately under the assumption that the states of the other blocks can be given, for example, from available observation data. After each block had gained a certain quality level, it became possible to integrate some of them in pairs, for example, the atmospheric and ocean dynamics, the atmospheric dynamics and chemistry. After further improvement and mutual adjustment of such models, it became possible to integrate all blocks of the Earth system into a single model. Such is the model presented in this paper. The aim of the paper is to show that all the components of the Earth system function in concord and the model as a whole is close to the actual climatic system in many characteristics. At the same time, one should bear in mind that an exhaustive description of each block and the results of its work cannot be presented *

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