The quantification of diurnal and seasonal gas (NH3, H2S, and CO2) and PM10 concentrations and emission rates (GPCER) from livestock production facilities is indispensable for the development of science-based setback determination methods and evaluation of improved downwind community air quality resulting from the implementation of gas pollution control. The purpose of this study was to employ backpropagation neural network (BPNN) and generalized regression neural network (GRNN) techniques to model GPCER generated and emitted from swine deep-pit finishing buildings as affected by time of day, season, ventilation rates, animal growth cycles, in-house manure storage levels, and weather conditions. The statistical results revealed that the BPNN and GRNN models were successfully developed to forecast hourly GPCER with very high coefficients of determination (R2) from 81.15% to 99.46% and very low values of systemic performance indexes. These good results indicated that the artificial neural network (ANN) technologies were capable of accurately modeling source air quality within and from the animal operations. It was also found that the process of constructing, training, and simulating the BPNN models was very complex. Some trial-and-error methods combined with a thorough understanding of theoretical backpropagation were required in order to obtain satisfying predictive results. The GRNN, based on nonlinear regression theory, can approximate any arbitrary function between input and output vectors and has a fast training time, great stability, and relatively easy network parameter settings during the training stage in comparison to the BPNN method. Thus, the GRNN was characterized as a preferred solution for its use in air quality modeling.