In this paper, the data of sunspot areas recorded at the US Air Force National Oceanic and Atmospheric Administration during solar Cycles 22 and 23 (1986 September 1 to 2007 August 31) have been analysed to investigate the midterm periodicities. Power spectral analysis has been performed separately for the data of the whole disc, and the northern and southern hemispheres of the Sun, which provides evidence for a multitude of quasi-periodic oscillations. During Cycle 22, in the high-frequency range, this covers the solar rotation periods, and shows prominent 27-41 d periods in both hemispheres for rising and declining phase of the solar cycle. In the intermediate-frequency range, we have detected a series of significant quasi-periodicities of 87-106, 159-175, 194-219, 292-318 and ∼389 d in different phases of Cycle 22. This result shows that well-known 'Rieger periodicity' of 150-160 d was present in sunspot activity even in solar cycle 22 but localized mainly in the southern hemisphere. When Cycle 23 is considered, it is found that a short-term periodicity having range of 24-45 d occurred in both rising and descending epochs in all hemispheres. On the other hand, in intermediate range, periods of 69-95, 113-133, 160-187, 245-321, 348-406 d and ∼1.3 yr were detected. This analysis provides evidence that the Rieger period reappeared in Cycle 23 but is predominant in the southern part of the Sun. Periods near 1.3 yr, which were reported in the rotation rate at the base of convection zone, have been found in the southern hemisphere only during minimum phase of Cycle 23. When time series of combined solar Cycles 22 and 23 were analysed, intermittent periods in the range of 24-43, 50-73, 86-120, 130-180, 240-270 d and quasi-annual period of 330-380 d were detected in all the data sets. Possible explanations of these observed periodicities are delivered on the basis of solar r-mode oscillation. © 2008 RAS.