In this talk we introduce the Pontryagin type C^0-Finsler structures on a differentiable manifolds, which are a generalization of Finsler structures. This structure satisfies the minimun requirements of Pontryagin’s maximum principle for the problem of minimizing paths. We define the extended geodesic field E on the slit cotangent bundle T*M\0 of the manifold, which is a generalization of the geodesic spray of Finsler geometry. We study the case where E is a locally Lipschitz vector field. Finally we show some examples where the geodesics on (M,F) are more naturally represented by E than by a similar structure on TM.