Summary: This article deals with an initial-boundary value problem for the coupled chemotaxis-haptotaxis system with nonlinear diffusion \[ \begin{cases} u_t=\nabla \cdot (D(u)\nabla u) -\chi\nabla \cdot (u\nabla v)- \xi\nabla\cdot (u\nabla w)+\mu u(1-u-w), &\quad x\in\Omega,\, t>0,\\ v_t=\Delta v-v+u, &\quad x\in\Omega,\, t>0,\\ w_t=-vw &\quad x\in\Omega,\, t>0, \end{cases} \] under homogeneous Neumann boundary conditions in a bounded smooth domain \(\Omega \subset\mathbb R^n\) , \(n=2\), 3, 4, where \(\chi\), \(\xi\) and \(\mu\) are given nonnegative parameters. The diffusivity \(D(u)\) is assumed to satisfy \(D(u)\geqslant \delta u^{m-1}\) for all \(u>0\) with some \(\delta >0\). It is proved that for sufficiently regular initial data global bounded solutions exist whenever \(m>2-\frac{2}{n}\). For the case of non-degenerate diffusion (i.e. \(D(0)>0\)) the solutions are classical; for the case of possibly degenerate diffusion \((D(0)\geqslant 0)\), the existence of bounded weak solutions is shown.