  Under a pulled-back approach given in [1] and firstly presented in [2], we
introduce, in this paper, the concepts of almost contact and normal almost
contact Finsler structures on the pulled-back bundle. Properties of structures
partly Sasakians are studied. Using the hh-curvature tensor of Chern connection
given in [2], we obtain some characterizations of horizontally Finslerian
K-contact structures via the horizontal Ricci tensor and the flag curvature.
