The paper describes the results of using Raman spectroscopy to study the canvases of Russian avant-garde artists. The study aimed to identify stable signs of paints for the recognition of counterfeits. The subject of the research was zinc white as a component of paints used by the 20th-century Russian avant-garde. Temporal changes occurring with them are due to chemical reactions of organic paint components with whites and with each other. The study shows that Raman spectroscopy is the most sensitive method for detecting ZnO time markers. Its results are compared with the results of pyrolysis–gas chromatography, mass spectrometry, and X-ray analysis of paints from paintings from the Russian avant-garde of the early, middle, and late twentieth century. The study results demonstrate that the paint compositions of the early and late 20th Century have significant similarities. The result of their aging is the appearance of products of thermal desorption and pyrolysis in the form of a homologous series of alcohols and aromatic hydrocarbons formed during the destruction and oxidation of oleic, linoleic, linolenic, palmitic, stearic acids, and/or azelaic acid. These acids are found in flaxseed oil. Zinc white of the early 20th century contains significant additions of gypsum. The composition of the components of mid-century paints is much less diverse. Genuine paintings contain homologous series of fatty acids sorbed on zinc oxide. The paper analyzes historical reasons for this phenomenon. The research shows that one of the stable signs of falsification is the use of titanium white and organic catalysis products based on them. The results of gas chromatography and mass spectrometry and Raman spectroscopy are supplemented by X-ray phase and X-ray fluorescence analysis. The paper provides detailed reference data on the spectra of Raman light scattering, thermal desorption, and pyrolysis of paints of the studied canvases and shows the differences in the mass spectra of genuine paintings and falsifications.