Summary: Let \(B(X)\) denote the algebra of all bounded linear operators on an infinite-dimensional separable complex Banach space \(X\) and \(M\) be a nonzero subspace of \(X\). We will characterize properties of being \(d-M\) mixing for a \(N\geq 2\) sequence \(T_{1,j},T_{2,j},\ldots, T_{N,j}\) of operators in \(B(X)\). Also, we will give necessary and sufficient conditions for a \(N \geq 2\) sequence \(T_{1,j},T_{2,j},\ldots,T_{N,j}\) of operators in \(B(X)\) to satisfy \(d- M\) universality criterion in terms of d-M topologically transitivity of this sequence.