In this paper, we study a compressible chemotaxis-convection model with sensitivity functions for tumor angiogenesis system, arising as a simplified model for the initial phase of tumor-related angiogenesis. As essential characteristics, this system is the existence of a sequential coupling between two chemical attraction processes, that involve the production of a signal, as in classical Keller-Segel systems, and are linked to another repulsive mutual diffusion mechanism, driven by the frictional force. The existence and uniqueness of solution for this system is established by the classical energy method........... ....................... Keywords: .................chemotaxis; attraction-repulsion; tumor angiogenesis.