A dynamic model of biogeochemical carbon cycles in swamp ecosystems is proposed. There are fast and slow biogeochemical cycles. Fast cycles operate in the biosphere and include photosynthesis, vegetative growth, and decomposition. Swamp ecosystems are one of the significant reservoirs of biogeochemical cycles. It is known that huge reserves of carbon in the form of slightly decomposed organic matter are preserved in the swamps. They are active sources of methane and carbon dioxide runoff from the atmosphere. Mathematical models of dynamic processes in ecology can be divided into two categories: quantitative and qualitative. Quantitative models, as a rule, are aimed at solving problems of predicting numerical indicators of the dynamics of real systems. They must be modified to consider specific climatic conditions, special types of swamp vegetation, and hydrological regime for their successful application. Qualitative models written as systems of differential equations assume the finding of singular points, their classification and study for stability, the construction of phase portraits, etc. Such models rarely lend themselves to quantitative verification, but provide important knowledge and understanding of processes in nature. A qualitative study of the system of ordinary differential equations describing carbon cycles is carried out, the types of singular points are investigated, integral curves and phase portraits are constructed.