By using Riccati transformation and the integral averaging technique, some new Kamenev-type oscillation criteria are established for the super-linear matrix differential systems X ″ ( t ) + ( X n ( t ) Q ( t ) X ∗ n ( t ) ) X ( t ) = 0 and X ″ ( t ) + ( X ∗ n ( t ) Q ( t ) X n ( t ) ) X ( t ) = 0 , t ⩾ t 0 > 0 , n ≥ 1 , where Q ( t ) is an m × m continuous symmetric and positive definite matrix for t ∈ [ t 0 , ∞ ) . The results improve and complement those given by Tomastik [E.C. Tomastik, Oscillation of nonlinear matrix differential equations of second-order, Proc. Amer. Math. Soc. 19 (1968) 1427–1431], Ahlbrandt et al. [C.D. Ahlbrandt, J. Ridenhour, R.C. Thompson, Oscillation of super-linear matrix differential equation, Proc. Amer. Math. Soc. 105 (1989) 141–148] and Ou [L.M. Ou, Atkinson’s super-linear oscillation theorem for matrix dynamic equations on a time scale, J. Math. Anal. Appl. 299 (2004) 615–629], which is illustrated by an example at the end of the paper.