This article is concerned with one of the most topical problems of modern astrophysics, that of elucidating the nature of the ``anomalous'' cosmic radiation in the radio-frequency lines of OH and H$_2$O, and it reviews the observational material and theoretical studies in this field up to 1973, inclusive. The fundamental features of the radio-frequency radiation of OH and H$_2$O are interpreted on the basis of the generally accepted concept of a natural cosmic maser. The fundamental relationships are derived that describe the amplification process in a cosmic traveling-wave maser. The most realistic of the proposed models of pumping of the inverted population of levels are discussed in detail. Considerable attention is paid to possible manifestions of nonlinear effects and to the reasons for the observed non-steady-state nature of the radiation. The cosmogonic aspect of the problem is treated in detail; arguments are given to favor the ``youth'' of the maser sources and their relation to regions of star and planet formation.