Modulation doped heterostructures GaAs/GaAs$_{1-x}$Nx/GaAs/Al0.3Ga0.7As:δSi with GaAs$_{1-x}$Nx Quantum Wells (QW) with different nitrogen contents x have been grown by molecular beam epitaxy and investigated by photoluminescence (PL) spectroscopy. We have found that at low temperature the photoluminescence spectra are essentially formed by two structures observed at 1.51 eV and 1.47 eV attributed to excitonic transitions in GaAs layer, and in GaAs$_{1-x}$Nx QW, respectively. The Band Anticrossing Model (BAC) has been adopted in order to confirm the nature of the transitions in GaAs$_{1-x}$Nx QW's. The band structure of $\delta $-doped GaAs/GaAs$_{1-x}$Nx/GaAs/Al0.3Ga0.7As:δSi has been studied theoretically by using the finite differences method to self-consistently and simultaneously solve Schrödinger and Poisson equations written within the Hartree approximation. We find in this way good agreement between our measured and our calculated values for the transition energies in our GaAs$_{1-x}$Nx QW's.