This paper proposes two models of a general nonlinear within-host Chikungunya virus (CHIKV) dynamics. The production, incidence, proliferation and removal rates of all compartments are modeled by general nonlinear functions that satisfy a set of reasonable conditions. The second model takes into consideration two forms of infected host cells: (i) latently infected cells which do not produce the CHIKV, (ii) actively infected cells which generate the CHIKV particles. We show that all the solutions of the models are nonnegative and bounded. The global stability of the steady states of the models is proven by applying Lyapunov method and LaSalle's invariance principle. We perform numerical simulations to complement the obtained theoretical results.