The chapter provides materials for the improvement of the vibroacoustic condition monitoring of complex rotating system during operation, such as, aviation gas-turbine engines (GTE). It is based on the development of theoretical basis of the vibroacoustical diagnosis methods, the application of the modern multi-level signal processing methods and neural networks for decision making. The low-frequency vibration and acoustic noise in the range 0–25 kHz is used as diagnostic information. Signal processing was performed using simulated vibroacoustic signals at the steady-state and non-steady-state modes of GTE in order to diagnose the initial crack-like damage of the blade. First, an analysis of the capabilities of different types of neural networks to recognize the technical condition of one blade without damage and with initial crack-like damage based on the two-dimensional vector of diagnostic features obtained using the free oscillation method was performed. The following neural networks showed the best result of nonlinear division of the plane of diagnostic features into classes: a two-layer neural network and a probabilistic neural network. Next, a probabilistic neural network was used to recognize the technical condition of the blades of the impeller based on the results of determining the dimensionless characteristics of elements of the wavelet decomposition of vibroacoustic signals in the steady-state and non-steady-state modes. A probabilistic neural network was also used to recognize the technical condition of the blades of the impeller based on the results of evaluating the bispectrum module of vibroacoustic signals in the steady-state mode. As a result of the study, the high efficiency of the probabilistic neural network was proven and the conditions for error-free recognition of the state of the blades were determined. The recognition of the technical condition of blades based on the bispectrum module estimates is carried out by a neural network of adaptive resonance theory, the use of which also ensures error-free classification in a certain range of values of the similarity parameter. The obtained results can be used to build a classifier and to improve the systems of condition monitoring of complex rotating system during operation.