| This paper deals with a chemotaxis-haptotaxis model of cancer invasion of tissue, initially proposed by Chaplain and Lolas. The model consists of a 3 x 3 reaction-diffusion-taxis partial differential equations describing interactions between cancer cells, matrix degrading enzymes, and the host tissue, and it includes two bounded nonlinear density-dependent chcmotactic and haptotactic sensitivity functions. The local exis-tence and uniqueness of solutions is first proved by the fixed point theorem. Then, based on Schauder theory and Lp theory of parabolic equations, the global existence and uniqueness of classical solutions to this model is showed. Furthermore, the bound-edness for a volume-filling model is studied.
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