  We find new non-Abelian flux tube solutions in a model of $N_f$ scalar fields
in the fundamental representation of SU(N)xU(1) with $N \leq N_f$ (the
``extended non-Abelian Higgs model''), and study their main properties. Among
the solutions there are spinning strings as well as superconducting ones. The
solutions exist only in a non trivial domain of the parameter space defined by
the ratio between the SU(N) and U(1) coupling constants, the scalar
self-interaction coupling constants, the magnetic fluxes (Abelian as well as
non-Abelian) and the ``twist parameter'' which is a non-trivial relative phase
of the Higgs fields.
