ASIPs and reconfigurable processors are architectural choices to extend the capabilities of a given processor. ASIPs suffer from fixed hardware after design, while ASIPs and reconfigurable processors suffer from the lack of a pre-established instruction set, making them difficult to program. As intermediate choice, reconfigurable coprocessors systems (RCSs) contain dedicated hardware (coprocessors) coupled to a standard processor core to accelerate specific tasks, allowing inserting or substituting hardware functionalities at execution time. This paper proposes a generic model for RCSs, targeted to reconfigurable devices with self-reconfiguration capabilities. A proof-of-concept case study is presented as well.