The paper focuses on the problem of analyzing spacecraft telemetric information solved by wavelet transform, reveals the prerequisites for automating the analysis process, and indicates the possible results of implementing algorithms for analyzing the state of spacecraft onboard systems according to the proposed method. To detect abnormal changes in telemetric parameters, we propose an algorithm for automated processing of their values; to analyze reliable data on the state of spacecraft onboard systems, we describe the step-by-step process of wavelet filtering of telemetric parameters time series. The study also introduces the ways to identify and eliminate faulty values in telemetric information. The method for automating the analysis process is based on the developed special mathematical apparatus; the paper briefly describes the mathematical transformations used in the study. We tested the method by analyzing the archival spacecraft telemetric information. The test results are given, as well as the results of the wavelet analysis of the telemetric parameters of the air conditioning system and the power supply system of the ISS Russian Segment.