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A mathematical model describing the coupling of electrical, optical and thermal effects in semiconductor lasers is introduced. Through a systematic asymptotic expansion, the governing system of differential equations is reduced to a single second-order boundary value problem. This highly nonlinear equation describes the time-independent maximum temperature in the boundary layer adjacent to the mirror facet. The solution of the problem is a multi-valued function of current. The graph of the maximum steady-state temperature as a function of current gives a fold-shaped response curve, which indicates that no bounded steady state exists beyond a critical value of current. For certain device parameters and initial conditions, thermal runaway occurs. A mechanism for the sudden mode of semiconductor laser failure is described in terms of thermal runaway. © 2000 American Institute of Physics.