Most of his work Velidov worked as a teacher of the Higher School of the KGB (now the FSB Academy). In 1971 he defended his doctoral thesis in 1973 was promoted to professor. Along with teaching Velidov actively engaged in studying the history of the Cheka during the Civil War, helped by his access to the archives of this organization. He is the author of numerous articles, publications and monographs on the subject. Velidova Proceedings distinguishes a deep knowledge of the subject, the conclusiveness. He sought, relying on the documents, objective coverage of events full of dramatic stories of the Cheka, showing not only positive, but also negative aspects of its operations.