A system of non-linear partial differential equations modeling tumor invasion into surrounding healthy tissue is analyzed. The model focuses on key components involved in tumor cell migration and takes into account cell motility and haptotaxis. The latter means the directed migratory response of tumor cells to the extracellular environment. Individual cell processes are modeled according to cell age. The equation for the tumor cell density thus incorporates second-order terms representing diffusion and taxis as well as a first-order part due to cell aging. Global existence and uniqueness of nonnegative solutions is shown.