  The North-South asymmetry of solar activity is variable in time and strength.
We analyse the long-term variation of the phase lags of hemispheric cycles and
check a conjectured relationship between these phase lags and the hemispheric
cycle strengths. Sunspot data are used from cycles 12-23 in which the
separation of northern and southern hemispheres is possible. The centers of
mass of the hemispheric cycle profiles were used to study the phase relations
and relative strengths of the hemispheric cycles. This approach considers a
cycle as a whole and disregards the short-term fluctuations of the cycle time
profile. The phase of the hemispheric cycles shows an alternating variation:
the northern cycle leads in 4 cycles and follows in 4 cycles. No significant
relationship is found between the phase and strength differences of the
hemispheric cycles.
  The period of 4+4 cycles appears to be close to the Gleissberg cycle and may
provide a key to its physical background. It may raise a new aspect in the
solar dynamo mechanism because it needs a very long memory.
