In this paper, we investigate the stability and instability for a generic non-conservative compressible two-fluid model. Under the condition that the initial fraction densities are close to the constant equilibrium state in H3∩

and the initial velocities are small in H2∩

̇, we establish the global existence and large time behavior of strong solutions by the energy method if0≤s<1/2. On the other hand, we show that the steady-state is nonlinear unstable in the sense of Hadamard if 1/2<s≤1.