Let M be a differentiable manifold, T x its tangent space at ε and TM={(x,y);x M; y M} bundle. A C 0 -Finsler structure is continuous function F:TM → [0, ∞ ) such that F(x, · ):T an asymmetric norm. In this work we introduce the Pontryagin type structures, which are structures satisfy minimum requirements of Pontryagin's maximum principle for problem minimizing paths. We define extended geodesi...