Our results of further calculations of the daily X-ray flare index (XFI) are presented, as well as the analysis of behaviour of XFI during the solar cycles 21—23, in comparison with the index of daily numbers of X-ray flares N_x, and with Wolf's numbers W. The A cross correlation function of the W and XFI indices is shown to be nearly symmetric for the solar cycle 22, while for the solar cycles 21 and 23, asymmetry of the cross correlation function indicates that there is a time lag of the X-ray flare activity with respect to the sunspot activity, with a characteristic value of about T = 10 months. Power spectra of the XFI, W, and N_x time series are studied. A statistically significant maximum corresponding to a period of about 150 days is found to have a complicated shape. The maximum is observed in the power spectra of all the three indices for the solar cycles 21 and 23, but it is not detected for the cycle 22. In the power spectra of N_x related to the minima of the solar cycles 21 and 22, the peaks corresponding to periods of about 225, 88, and 53 days dominate.