In this talk we will discuss matrix models which admit, on top of the usual ’t Hooft expansion, an M-theory-like expansion, i.e. an expansion at large N but where the rest of the parameters are fixed. We will discuss general aspects of these type of matrix integrals and we will analyze in detail two different examples: first, the matrix model computing the partition function of N=4 supersymmetric Yang–Mills theory in three dimensions with one adjoint hypermultiplet and Nffundamental. Second, a similar model which arises in the study of statistical systems in two dimensions.