A theory is developed for the luminescence linewidth in a quantum well made of ternaries when the two-dimensionally free excitons undergo alloy disorder scattering. The expression for linewidth shows a L-1 dependence on the well width L for infinite barrier height. For thin wells leakage of wave function into the barrier is considered. A comparison between the experimental data and the present values points out the dominant role of alloy disorder scattering. For wells thinner than 40 Å the calculated values decrease with decreasing well width, indicating the importance of surface roughness scattering.