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The subject of this paper is the existence and stability of solar cycles with duration in the range of 20-250 years. Five type of data series are used: 1) The Zurich series (1749-2009), the mean annual International sunspot number Ri; 2) The Group sunspot number series Rh (1610-1995); 3) The simulated extended sunspot Rsi number from Extended time series of Solar Activity Indices (ESAI) (1090- 2002); 4) The simulated extended geomagnetic aa-index from ESAI (1099-2002); 5) The Meudon filament series (1919-1991) (it is used only particularly). Data series are smoothed over 11 years and supercenturial trends are removed. Two principally independent methods of time series analysis are used: the T-R periodogram analysis (both in the standard and "scanning window" regimes) and the wavelet-analysis. The obtained results are very similar. It is found that in all series a strong cycle with mean duration of 55-60 years exists. It is very well expressed in the 18th and the 19th centuries. It is less pronounced during the end of the 19th and the beginning of the 20th centuries. On the other hand a strong and stable quasi 110-120 years and ~200-year cycles are obtained in most of these series. However the 200-yr cycle is not detectable in the Zurich series. There is a strong mean oscillation of ~ 95 years, which is absent in the other data sets. The analysis of the ESAI (AD 1090-2002) proved that the quasi century cycle has a relatively stable doublet (~80 and ~120 years) or triplet (~55-60, 80 and 120 years) structure during the last ~900 years. Most probably the different type of oscillations in the sub-century and century period range corresponds to cycles of different classes of active regions. The solar-terrestrial relationships aspects of these results are briefly discussed., 25 pages +17 figures + 1 table