Article is dedicated to the history of the development of the theory of economic crises with capitalism. Two directions in the development of economic science are separated. One direction represent the scientific schools, which deny the objective bases of the crises of overproduction in the market economy and the developing models crisis- free developments. Opposite direction adhere to the scientific schools, which recognize the presence of the objective reasons for crises that is of practical use for producing the effective anti-crisis actions. The study by conclusion about the updating of politico-economic approach to the analysis of last world crisis and its consequences is generalized. Its realization predetermines special attention to the different versions of the appearance of the accumulation of capital, which played the key role in the origin of crisis processes in the world economy.