Despite the triumph of capitalism in economic competition with communism, recent years have shown the increasing contradictions of the former, the most serious of which is the growth of social inequality. All of this requires the comprehension of possible alternatives to capitalism. The authors consider these possible alternatives in the framework of the market economy, which has proven itself as the best system in terms of the optimal use of rare resources. The difference between the market economy as such and its private manifestation, capitalism, lies in the form of ownership. Moreover, capitalism is based on private ownership, however, versions of the market economy with other forms of ownership are possible. Making use of basic methodological principles of economic science, the authors analyse the pros and cons of private and other forms of ownership in the framework of the market economy. The former’s strengths lie in the initiative to create new companies and the drive to increase efficiency, while its weaknesses lie in the growth and entrenchment of social inequalities. The strength of the market economy with other forms of ownership is a lesser degree of inequality, however, its weaknesses are insufficient incentives for innovation and growth. In today’s world, only capitalism fully realises the principles of the market economy. Economic schemes based on other forms of ownership demonstrate substantial deviations from these principles, and therefore exist only in theories so far. To make an alternative to capitalism feasible, forms of the market economy with other systems of ownership must override their a-priori shortcomings, the main shortcoming of which consists of insufficient incentives for risk acceptance and efficiency gains.