NB: santraukoje neįsikelia formulės! The graduation paper examines frame bundles B (Vn ), whose base is n–dimensional differential manifold Vn and the first differential extensions of this stratification J1B(Vn). The bundle of frames is normalized by way of linear connection object F ; provided this object is the linear function of coordinates p , then the linear connection of stratification B(Vn) defines affine connection Vn of reference space. The thesis analyses the overall linear connection and linear co-connection of stratification J1B(Vn) and related basal differentiations. It has been proven that the linear connection of bundle of frames B(Vn) indicates the linear connection and linear co-connection of extended stratification J1B(Vn), the relation between the ratios of the induced connection and the induced co-connection and the representation of the components of curvature objects of the obtained induced linear connection.