In 1940, after graduating the secondary school, Mozhayev enrolled into the shipbuilding faculty of the Gorky Institute of Navy Transport Engineers.
Even in his early works, according to critic Andrey Turkov, Mozhayev's approach differed from what was considered the norm: "instead of singing paeans to the 'achievements of Socialism', he was among the first to express deep concern about the consumerist attitude towards natural resources which was becoming more and more evident.
"[2][1] In 1961 Mozhayev's essay "The Land Awaits Its Master" caused controversy and Oktyabr magazine editor Fyodor Panfyorov had to approach one of Nikita Khrushchev's secretaries to receive the permission for the publication.
Mikhail Kedrov's production of Mozhayev's play Having Lied Once (Yedinozhdy solgav) was banned by the Soviet Ministry of Culture.
The publication of a sequel was cancelled by the Minister of Culture Ekaterina Furtseva personally who (despite the Central Committee member Dmitry Polyansky's efforts to save it) declared it a parody on the Soviet way of life.