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We present an analysis of the steady-state operation of a two-element coupled-cavity laser near a mode hop. The equations of motion for the two cavities and two relevant modes of a longitudinally coupled-cavity laser are reduced to a system of nondimensional nonlinear ordinary differential equations which describe a general two-element laser. The equations are then solved and the stability of their solutions is analyzed. Depending upon the fill factors for the two modes, there exists an intrinsically multimode oscillation for operating conditions under which it was previously thought that no steady state existed. Under conditions where the multimode state is unstable, both of the single-mode states are stable with bistable transitions occurring only on the boundaries of the unstable multimode regimes.