  In this paper we show that the topological closure of the holonomy group of a
certain class of projectively flat Finsler 2-manifolds of constant curvature is
maximal, that is isomorphic to the connected component of the diffeomorphism
group of the circle. This class of 2-manifolds contains the standard Funk plane
of constant negative curvature and the Bryant-Shen-spheres of constant positive
curvature. The result provides the first examples describing completely
infinite dimensional Finslerian holonomy structures.
