In the frame of this study, the problem of detecting the anomalies in nonstationary process signals as earlier signs of equipment faults and breakdowns is considered. The approach to the detection of anomalies by using the Hilbert–Huang transform in combination with the statistical model is presented. The main idea of this approach consists in analyzing the statistical parameters of the elements of Hilbert–Huang transform, which is adaptive in the case of nonstationary data and provides high itemization in the frequency-time region. The schematic layout and algorithm of this approach, the statistical classification model, the numerical calculations on model and real data, and the comparative analysis with other methods of detecting the anomalies in signals are described.