We present a comprehensive study of longitudinal transport of two-dimensional (2D) carriers in n- and p-type modulation doped Ga(x)In(1-x)N(y)As(1-y) /GaAs quantum well structures. The Hall mobility and carrier density of electrons in the n-modulation doped quantum wells (QWs) decreases with increasing nitrogen composition. However, the mobility of the 2D holes in p-modulation doped wells is not influenced by nitrogen and it is significantly higher than that of 2D electrons in n-modulation doped material. The observed behaviour is explained in terms of increasing electron effective mass as well as enhanced N-related alloying scattering with increasing nitrogen content. In order to determine the conduction band (CB) and valence band (VB) structures as well as electron and hole effective masses, the band anticrossing model with an eight-band [Formula: see text] approximation in the Lüttinger-Kohn approach is used. The effects of strain, quantum confinement and the strong coupling between the localized nitrogen states and the CB extended states of GaInAs are considered in the calculations. The results indicate that the nitrogen induces a strong perturbation to the CB of the matrix semiconductor whilst the VB remains unaffected. The temperature dependent mobility of 2D electron gas is discussed using an analytical model that accounts for the most important scattering mechanisms. The results indicate that the interface roughness and N-related alloy scattering are the dominant mechanisms at low temperatures, while polar optical phonon and N-related alloy scattering limit mobility at high temperatures.