Abstract: The energies and the nonradiative linewidths of the electron-hole quasibound states in narrow GaAs-based quantum wells are calculated by the exterior complex-scaling technique. These states appear in the continuous spectrum of the in-plane relative electron-hole motion, above the well-known exciton states. The nonradiative linewidths of the obtained quasibound states are estimated to be less than 0.1 meV.