The methods currently used in the investigation of the inequalities of the Earth's rotation during the last twenty years were those of spectral analysis of random functions. This led to the discovery of several periodical inequalities for which no clear explanation has always been found. However well known hypothesis which, strictly speaking, do not fit the nature of the analysed data are underlying the methods used by the quoted authors, in most cases Blackman-Turkey method or Fourier method. If the period of a given component is variable, peaks appear in the spectrum at various places, whereby one might erroneously believe that they belong to different harmonic terms. The selectivity functions display so called secondary peaks, whose amplitude are often not negligible. An example will appear later when parasitic peaks, generated by the term of period P = 3.5 years, will be analysed. The, amplitudes of most of the newly discovered terms are small which make it necessary to check the reality of their identification, on the condition that new data and new methods are used. Basic data used in this paper are raw differences UT2-UTC given ever five days for the period 1967.0-1978.0, which are published by the BIH in ANNUAL REPORTS (AR). To avoid the difficulties resulting from the jumpill changes of UT2-UTC as well as from chariges due to the adjustment of UTC, transition to the UT2-T AI system was made by using the relations between UT and TAl (RAPPORT ANNUEL, 1977, Table 10, p. B-27).