Frequency analog of correlation coefficient of two random processes, i.e. the coherence function has been used for statistical power evaluation of the linear connection of the state variables of the induction motor. Analysis of the calculated coherence function values with using the smoothed correlation functions and averaging over the group of processes implementation allowed us to conclude about the reasonability of using a time window bounded by quarter period of the input voltage to produce significant differences in the work of linear, close to linear and nonlinear systems. The study of the coherence function values in different modes can allow us to determine the boundaries of parameter values for which the system retains the linear properties. The experimental results confirmed the validity of assumptions about the possibility of assessing the system linearity. The carrying out of continuous monitoring of the system properties allows us to notice the deterioration of linear properties. In addition, the achieving of coherence function values less than 0.9 will be indicate about decreasing of linear properties: the appearance of higher harmonics in the stator current, power and torque of the induction motor, and, in fact, decrease of energy efficiency. The results of the research can be the basis for monitoring systems of induction motors condition.