In a subspace $GR_M$ of a generalized Riemannian space $GR_N$ we observe, a familly of tensor fields (1.1), which contains as particular cases tangent and normal vectors of the subspace as well the curvature, vector $q^\alpha$ of a curve, in the subspace. Because of non-symmetry of Cristoffel symbols we define four kinds of derivational formulas of the above mentioned familly, as well six integrability conditions of these formulas. As particular cases one obtains Gauss--Codazzi equations of the subspace and corensponding equations for $q^\alpha$. In this manner derivational formulas of Riemannian space are generalized, as well as their integrability conditions, i.e. the Gauss--Codazzi equations.