Аннотация:Abstract. It is proved that the graded Lie algebras of innitesimal holomorphic automorphisms ofa nondegenerate quadric of codimension k do not have weight components more than 2k. It is alsoproved that, for k ⩽ 3, there are no graded components of weight greater than 2. Several questionsare formulated. DOI 10.1134/S1061920821030043