 In 1960, he tied for 14–15th at the 27th USSR championships in Leningrad won by Korchnoi.Nei won the Baltic Republics championships in 1961 in Palanga, in 1962 in Tartu, in 1963 in Estonia, and in 1964 in Pärnu.In 1964 he also tied for first with Keres in Beverwijk (Corus chess tournament).