This work reports a compact behavioral model for the hysteretic conduction characteristics of Al/Gd_0.1Ca_0.9MnO₃(GCMO)/Au resistive switching devices suitable for SPICE simulations. The devices are nonvolatile, forming-less, compliance-free, and self-rectifying multistate memristive structures which makes them of maximum interest for neuromorphic computing and memory applications. The proposed model relies on two coupled equations, one for the electron transport and a second one for the vacancy displacement. The proposed model considers a novel approach for solving the internal state of the device based on the so-called generalized quasi-static hysteron whose application can be extended to other structures and dynamics in addition to the ones discussed here.