For a higher order linear
quasi-differential equation which is non-self-adjoint there is presented a disconjugacy
criterion that is a consequence of the disconjugacy of an associated self-adjoint
quasi-differential equation. In particular, there is considered the specific form of this
criterion for a higher order differential equation of the canonical form which has been
presented by the author, Transactions of the American Mathematical Society, 85
(1957), 446-461.