The analyst often must deal with data that represents the history of changes in various objects over time, with time series. They are the ones that are most interesting from the point of view of many analysis tasks, and especially forecasting. For analysis tasks, time counts are of interest-values recorded at some, usually equidistant, points in time. Counts can be taken at various intervals: in a minute, an hour, a day, a week, a month, or a year, depending on how much detail the process should be analyzed. In time series analysis problems, we are dealing with discrete time, when each observation of a parameter forms a time frame. We can say the same about the behavior of COVID-19 over time. This paper solves the problem of predicting COVID-19 diseases in Moscow and the Russian Federation using neural networks. This approach is useful when it is necessary to overcome difficulties related to non-stationarity, incompleteness, unknown distribution of data, or when statistical methods are not completely satisfactory. The problem of forecasting is solved using the analytical platform Deductor Studio, developed by specialists of Intersoft Lab of the Russian Federation. When solving this problem, we used mechanisms for clearing data from noise and anomalies, which ensured the quality of building a forecast model and obtaining forecast values for tens of days ahead. The principle of time series forecasting was also demonstrated: import, seasonal detection, cleaning, smoothing, building a predictive model, and predicting COVID-19 diseases in Moscow and the Russian Federation using neural technologies for twenty days ahead.