In this paper there are discussed the three-component distributions of affine space $A_{n+1}$. Functions $\left\{{ℳ}^{\sigma }\right\}$, which are introduced in the neighborhood of the second order, determine the normal of the first kind of $\mathscr{H}$-distribution in every center of $\mathscr{H}$-distribution. There are discussed too normals $\left\{{𝒵}^{\sigma }\right\}$ and quasi-tensor of the second order $\left\{{𝒮}^{\sigma }\right\}$. In the same way bunches of the projective normals of the first kind of the $ℳ$-distributions were determined in the differential neighborhood of the second and third order.