The paper is a brief overview of the works by Iosif S. Shklovsky (1916--1985), carried out over almost 30 years (1955--1985), on the nature of activity (primarily in the radio frequency range) in nuclei of some galaxies. Worthy of note is Shklovskys pioneering work of 1962, in which he made an attempt to consider possible evolutionary tracks of extragalactic radio sources by constructing an analog of the Herzsprung--Russel diagram for stars (radio luminosity at 160 MHz was taken instead of optical luminosity; total radio size at the same frequency, as the other parameter). Later works by other authors are also discussed, where similar diagrams were plotted using a larger observational material. Special attention is paid to the evolution of Shklovskys views regarding the possible ways of gas getting into radio galaxies central regions, followed by high-velocity ejections of magnetized plasmons from their nuclei. In his assumptions, Shklovsky was mainly based on the observational data for the properties of the closest radio galaxy, NGC 4486 (Virgo A, M87), which he believed to be the same reference standard for extragalactic radio astronomy as the Crab Nebula for galactic radio astronomy. Shklovskys approach to the recurrence of the activity phenomenon in galactic nuclei and the one-sided character of radio ejections from them is discussed. Modern views on these issues are also briefly considered.
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