The paper deals with the multidimensional analog of the concept of nonlinear connectivity of order p, the content of the analog being that, for each m-submanifold of the basis of the principal fibration, there is defined a linear connectivity with horizontal m-distribution in the submanifolds passing through the common m_P-element of tangency. It has been possible to reduce consideration to the case of a linear connectivity in the appropriately chosen principal fibration.