In this thesis we study Sturm-Liouville problems, where the locally integrable coefficients are replaced by measure-valued ones. Classical derivatives of the Sturm-Liouville differential operator are replaced by Radon-Nikodym derivatives with respect to complex Borel measures. At the beginning, we consider initial value problems of ordninary linear differential equations of first order with Radon-Nikodym derviative with respect to a positive Borel measure. We develop subsequently the theory of Sturm-Liouville operators with measure-valued coefficients and find boundary conditions, so that the correspinding operator is self-adjoint. In the case of separate boundary conditions we solve the eigenvalue problem and obtain important results about the properties of the solution operator and the eigenvalues of the corresponding self-adjoint differential operator. Eventually we deal with the -v-Laplace operator, a special case of our previously considered operator, and study the asymptotic behaviour of its eigenvalue counting function, if is a self-similar measure and v fulfills certain homogenity conditions.