  The subject of this paper is the existence and stability of solar cycles with
durations in the range of 20-250 years. Five types of data series are used: 1)
The Zurich series (1749-2009 AD), the mean annual International sunspot number
Ri, 2) The Group sunspot number series Rh (1610-1995 AD), 3) The simulated
extended sunspot Rsi number from Extended time series of Solar Activity Indices
(ESAI) (1090-2002 AD), 4) The simulated extended geomagnetic aa-index from ESAI
(1099-2002 AD), 5) The Meudon filament series (1919-1991 AD) (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 all of these series except in Ri. In the last
series a strong mean oscillation of ~ 95 years is found, which is absent in the
other data sets. The analysis of the ESAI (1090-2002 AD) 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. An interesting
feature in all series is the existence of significant ~29-year cycle after the
last centurial Gleissberg-Gnevishev's minimum (1898-1923 AD). Most probably the
different types of oscillations in the sub-century and century period range
correspond to cycles of different classes of active regions.
