  We consider noncommutative gauge theories which have zero mass states
propagating along both commutative and noncommutative dimensions. Solitons in
these theories generically carry U(m) gauge group on their world-volume. From
the point of view of string theory, these solitons correspond to
  ``branes within branes''. We show that once the world-volume U(m) gauge
theory is in the Higgs phase, light states become quasi-localized, rather than
strictly localized on the soliton, i.e. they mix with light bulk modes and have
finite widths to escape into the noncommutative dimensions. At small values of
U(m) symmetry breaking parameters, these widths are small compared to the
corresponding masses. Explicit examples considered are adjoint scalar field in
the background of a noncommutative vortex in U(1)-Higgs theory, and gauge
fields in instanton backgrounds in pure gauge noncommutative theories.
