This paper suggests a numerical model of the Gleissberg cycle based on a sp
herical shell dynamo. The formulation of the problem includes a description
both of the rotation law and of the hydromagnetic dynamo. The suggested mo
del allows the Gleissberg cycle to be interpreted as resulting from the mag
netic feedback on the angular momentum fluxes which maintain the rotation l
aw in the shell. The period of the long-term variations is determined by re
laxation properties of the shell. Hence, it is directly associated with the
time taken to re-establish the differential rotation after the magnetic pe
rturbations of the angular momentum transport.