We show that radial flows (directed either inward or outward) suppress mean
-field dynamo action in a thin disc. Under conditions typical of spiral gal
axies, the reduction in the growth rate of the large-scale magnetic field c
an reach 25-30%. The dynamo-generated galactic magnetic fields themselves c
an drive radial flows at a rate of order 0.1 M(.)yr(-1). These radial flows
can contribute to the saturation of the dynamo action together with other
nonlinear effects. We also present arguments, and an illustrative computati
on, to support the view that in the inner regions of barred galaxies the ma
gnetically driven mass accretion rate may be substantially larger than the
above estimate due to deviations of magnetic field from axial symmetry. The
magnetically driven inflow rate in barred galaxies can reach about 3 M(.)y
r(-1).