In this paper super-associative algebras with (2m,m)−quasigroup operations are considered. Case $m = 1$ is described in [1]. Super-associative algebras with n−quasigroup operations for $n = 3$ Yu. Movsisyan was described in 1984 (cf. [6]). Case $n \geq 3$ was described in [10]. See, also [11].