Beginning from Thomas Moore’s book Utopia in 1516, world social- ism has had a history of a little more than 500 years. The fact that the vast majority of European critical utopian socialists regard private ownership, commodity, money, and market as the root of evil is of great reflexive value. Marx, Engels, and Lenin all believed that dur- ing transition from the old society to a communist society (including socialism as the first or lower stage), private ownership, commodity and monetary relations could continue to exist in very small amounts. Only when private ownership, cooperative economy and commodity– money relations are completely eliminated can there formally be a communist society. This is the first concept of a socialist economic system, established by Marx, Engels and Lenin; it is a socialist social concept in a strict sense. Vietnam has so far adhered to this criterion for socialist society, declaring that it is still in the transition phase to socialism and not yet having achieved socialism. Of course, Lenin sometimes referred to the New Economic Pol- icy period, which contained a certain amount of private ownership, 180 SCIENCE & SOCIETY cooperative economy, and commodity economy, as socialism, but only in the special sense of the working class and its party being in power. Stalin, similarly, declared, in 1936, that socialism was achieved in the Soviet Union (Stalin, 1978), at a time when there still existed cooperative economy, commodity and monetary relations, and the issuance of money wages instead of labor vouchers. Mao Zedong agreed with the Soviet standard, and in 1956 declared the end of the transition period (the period of New Democracy) from the old society to socialist society. After China began its reform and opening up, the constitution in the 1990s stipulated the implementation of a property rights system that had public ownership as the center and non-public economy as an important part, and implementation of the socialist market economy. These steps further lowered the standard for socialist society. This is the third concept of a socialist economic system, established by Deng Xiaoping. As to whether non-public economy has surpassed public economy and become the main central form in reality, this is a ques- tion about the actual operation of the economy, about whether or not the country is strictly following the constitution, and about system adjustment. There is no right or wrong in the three views of the socialist economic system. They just represent different values and criteria for economic systems. I have tried to enrich the theory by, in a broad sense, defining the first concept of a socialist economic system as the advanced stage of socialism, the second as the intermediate stage, and the third as the primary stage. The idea of three stages of social- ism is based on previous research, based on the Marxist classics and on practical experience (for details see Cheng and Hu, 2018). This new theory answers, in a logically consistent manner, the difficult questions of what socialism is and how its practice and operation should proceed; it is intended to serve as the basis for further aca- demic research and practical undertaking. It obviously differs from views of “socialism without working-class rule,” “socialism–capitalism convergence,” “high welfare is socialism,” and “permanent primary stage of socialism.”