We introduce almost contact and cosymplectic Finsler manifolds. Then, we characterizealmost contact Randers metrics. It is proved that a cosymplectic Finsler manifold ofconstantag curvature must have vanishingag curvature. We prove that every cosym-plectic Finsler manifold is a Landsberg space, under a mild condition. Finally, we showthat a cosymplectic Finsler manifold is a Douglas space if and only if it is a Berwaldspace.
