  A supersymmetric non-Abelian self-dual gauge theory with the explicit
introduction of Kaluza-Klein modes is proposed to give a classical description
of multiple M5-branes on $R^5 \times S^1$. The gauge symmetry is parametrized
by Lie-algebra valued 1-forms with the redundancy of a 0-form, and the
supersymmetry transformations without gauge-fixing are given. We study BPS
configurations involving KK modes, including M-waves and M2-branes with
non-trivial distributions around the circle. Finally, this supersymmetric gauge
theory of two-forms can be equipped with more general non-Abelian gerbes in
five dimensions.
