The article represents a comparison of models based on a non-linear autoregressive neural network with external input (NARX) for time series forecasting. The networks were trained using three algorithms that are most applicable in such studies: Levenberg-Marquart (LM), Levenberg-Marquart with Bayesian regularization (BR), and gradient descent with adjustable speed parameters (GDA). For modeling and forecasting, data on the concentration of methane and carbon dioxide in the surface layer of atmospheric air on the arctic island Belyy, YNAO, Russia were used. A time interval of 190 hours was chosen with a one-hour lag. To train the NARX network, methane and carbon dioxide concentrations corresponding to the rst 170 hours of the interval were used. Then a forecast was made for the next 20 hours. Models based on the NARX network with the LM learning algorithm showed the highest forecast accuracy, as well as minimal errors and a fairly high learning rate for the both greenhouse gases.