As a research method, multi layer neural network (MLNN) configurations 41-1-Х-4 were used, where 41 is the number of input neurons; 1–the number of hidden layers; X–the number of hidden neurons; 4–the number of resultant neurons created using the Neural Network Toolbox of the MatLAB system, to detect U2R network attacks: y1–Rootkit attack, y2–Buffer overflow attack, y3–Loadmodule attack, y4–No attack. Using the open database of NSL-KDD network traffic parameters on the created MLNN, a study of its error and number of epochs at different number of hidden neurons (25, 35 and 45 was carried out using different training algorithms: Levenberg-Marquardt; Bayesian Regularization; Scaled Conjugate Gradient. It is determined that the smallest value of the MLNN error was based on the use of the hyperbolic tangent as a function of activating a hidden layer according by the Levenberg-Marquardt training algorithm, and it is enough to have 25 hidden neurons. An assessment of the quality of detection of U2R attacks on MLNN configuration 41-1-25-4 at its optimal parameters was carried out. It is determined that errors of the first and second kind are 9% and 10%, respectively.