We study theoretically the conditions under which optical bistability is achievable in a two-subband system in a semiconductor quantum well. We consider the interaction of the two-subband system with a continuous wave electromagnetic field, which induces intersubband transitions. For the description of the system dynamics we use the effective nonlinear density matrix equations. We solve these equations analytically, in the steady state, for a GaAs/AlGaAs quantum well structure. For several combinations of the values of the parameters three real solutions of the population inversion arise and the phenomenon of optical bistability prevails.