  We investigate a class of topological monoids with a suitable family of
characters which we call Feller topological monoids. We extend the classical
notion of subordinators to subordinators on Feller topological monoids. Under
suitable assumptions, we prove a L\'evy-Khintchine type representation for such
subordinators. In addition, a L\'evy-It\^o like decomposition is obtained.
These formulae generalize the classical ones for subordinators.
