  We consider gauge vortices in symmetry breaking models with a non-canonical
kinetic term. This work extends our previous study on global topological
k-defects (hep-th/0608071), including a gauge field. The model consists of a
scalar field with a non-canonical kinetic term, while for the gauge field the
standard form of its kinetic term is preserved. Topological defects arising in
such models, k-vortices, may have quite different properties as compared to
``standard'' vortices. This happens because an additional dimensional parameter
enters the Lagrangian for the considered model -- a ``kinetic'' mass. We
briefly discuss possible consequences for cosmology, in particular, the
formation of cosmic strings during phase transitions in the early universe and
their properties.
