We develop the theory of N -homogeneous algebras in a super-setting, with particular emphasis on the Koszul property. To any Hecke operator \mathcal R on a vector superspace, we associate certain superalgebras S_{\mathcal{R},N} and \wedge_{\mathcal{R},N} generalizing the ordinary symmetric and Grassmann algebra, respectively. We prove that these algebras are N -Koszul. For the special case where \mathcal{R} is the ordinary supersymmetry, we derive an N -generalized super-version of MacMahon’s classical “master theorem”.