In this project we will study products of random matrices that are not independent. In particular, we want to find out, if the statistics of the singular values and of the complex eigenvalues of the product matrix remain universal, which is important for applications. At the same time, the coupling between the random matrices that are multiplied shall enable us to find new scaling limits that are relevant e.g. for the Lyapunov exponents. Further applications to field theories with chemical potentials are planned.