Let $R$ be a commutative Noetherian ring, $I,J$ be two ideals of $R$, and $M,N$ be two $R$-modules. We study the cohomological dimension of $N,M$ with respect to $(I,J)$, denoted by ${\rm cd}(I, J, N, M)$, and we get some relations between this invariant and other types of cohomological dimensions.
