  The property of degeneration of modular graded Lie algebras, first
investigated by B. Weisfeiler, is analyzed. Transitive irreducible graded Lie
algebras $L=\sum_{i\in \mathbb Z}L_i,$ over an algebraically closed field of
characteristic $p>2,$ with classical reductive component $L_0$ are considered.
We show that if a non-degenerate Lie algebra $L$ contains a transitive
degenerate subalgebra $L'$ such that $\dim L'_1>1,$ then $L$ is an
infinite-dimensional Lie algebra.
