  We study the global evolution of the magnetic field and interstellar medium
(ISM) of the barred and ringed galaxies in the presence of non-axisymmetric
components of the potential, i.e. the bar and/or the oval perturbations. The
magnetohydrodynamical dynamo is driven by cosmic rays (CR), which are
continuously supplied to the disk by supernova (SN) remnants. Additionally,
weak, dipolar and randomly oriented magnetic field is injected to the galactic
disk during SN explosions. To compare our results directly with the observed
properties of galaxies we construct realistic maps of high-frequency polarized
radio emission. The main result is that CR driven dynamo can amplify weak
magnetic fields up to few $\mu$G within few Gyr in barred and ringed galaxies.
What is more, the modelled magnetic field configuration resembles maps of the
polarized intensity observed in barred and ringed galaxies.
