We present the results of longitudinal carrier transport under a high electrical field in n- and p-type modulation-doped Ga0.68In0.32NyAs1-y/GaAs (y = 0.009, 0.017) quantum well (QW) structures. Nitrogen composition-dependent drift velocities of electrons are observed to be saturated at 1.7 x 10(7)cm s(-1) and 1.2 x 10(7)cm s(-1) at 77 K for the samples with y = 0.009 and y = 0.017, respectively, while the drift velocities of holes do not saturate but slightly increase at the applied electric field in the range of interest. The hole drift velocity is observed to be higher than the electron drift velocity. The electron mobility exhibits an almost temperature-independent characteristic. On the other hand, the hole mobility exhibits a conventional temperature dependence of modulation-doped QW structures. As the temperature increases, the drift velocity of the electrons exhibits an almost an temperature-insensitive characteristic, but, on the other hand, for holes, drift velocity decreases approximately from 10(7)-10(6)cm s(-1). It is observed that the drift velocities of electrons and holes are N-dependent and suppressed at higher electric fields. Furthermore, experimental results show that there is no evidence of negative differential velocity (NDV) behaviour for both n- and p-type samples. To explore the observed electron and hole drift velocity characteristic at high electric fields, we use a simple theoretical model for carrier transport, which takes into account the effect of non-drifting hot phonons. The mobility mapping technique (comparison method) is used to extract hot hole temperature in order to employ it in the non-drifted phonon distribution and to obtain the drift velocity-electric field curves. Then hot electron temperatures are obtained from the drift velocity-electric field curves as a fit parameter using non-drifted hot phonon dynamics The analytical model is well-matched to the experimental upsilon(d)-E curves, indicating that carrier-hot phonon scattering is the main reason for suppressing the NDV mechanism in GaInNAs/GaAs QW structures with a carrier density higher than 10(17)cm(-3).