  Using a nonlinear mean-field solar dynamo model, we study relationships
between the amplitude of the `extended' mode of migrating zonal flows
(`torsional oscillations') and magnetic cycles, and investigate whether
properties the torsional oscillations in subsurface layers and in the deep
convection zone can provide information about the future solar cycles. We
consider two types of dynamo models: models with regular variations of the
alpha-effect, and models with stochastic fluctuations, simulating `long'- and
'short-memory' types of magnetic activity variations. It is found that
torsional oscillation parameters, such the zonal acceleration, show a
considerable correlation with the magnitude of the subsequent cycles with a
time lag of 11-20 yr. The sign of the correlation and the time-lag parameters
can depend on the depth and latitude of the torsional oscillations as well as
on the properties of long-term (`centennial') variations of the dynamo cycles.
The strongest correlations are found for the zonal acceleration at high
latitudes at the base of the convection zone. The model results demonstrate
that helioseismic observations of the torsional oscillations can be useful for
advanced prediction of the solar cycles, one-two sunspot cycles ahead.
