  We investigate the vortex structure assuming the d-density wave scenario of
the pseudogap. We discuss the profiles of the order parameters in the vicinity
of the vortex, effective vortex charge and the local density of states. We find
a pronounced modification of these quantities when compared to a purely
superconducting case. Results have been obtained for a clean system as well as
in the presence of a nonmagnetic impurity. We show that the competition between
superconductivity and the density wave may explain some experimental data
recently obtained for high-temperature superconductors. In particular, we show
that the d-density wave scenario explains the asymmetry of the gap observed in
the vicinity of the vortex core.
