The used numerical model takes into account two quantized energy levels, n = 1, 2 for electrons and heavy holes in the conduction and valence bands of a single quantum-well laser where spontaneous emission. Auger recombination, and nonlinear gain suppression are considered. The time evolution of photon densities, P 1 and P 2, connected with first and second quantized state lasing at subband transition energies E 1 and E 2, respectively, has been investigated for large-signal modulation of the injection current at various cavity losses. Within a relatively small interval of cavity loss pronounced two-mode emission ( P 1, P 2) with inclusion of period-doubling bifurcations has been found. Period-doubling routes to chaos with a period-3 window in the chaos, and bistable pairs of period-1/period-3 as well as period-2/period-6 attractors have been obtained in case of single-mode operation at photon energies E 1 and E 2, respectively.