with continuous coefficients on a t-interval I is said to be disconjugate on I if no solution (0-0) has n zeros on I. For n>2, most known results giving conditions which assure that (0.1) is disconjugate concern perturbations of un -=0 either for a fixed finite interval [as, e.g., in the theorem of de la Vallee Poussin (cf. [2, Exercise 5.3(d), p. 346])] or for large t. This paper deals with equations (1.1) which are perturbations of equations with constant coefficients, disconjugate on -00 < t < 00. As corollaries, we obtain theorems which are refinements of known results concerning perturbations of un -=0, but we do not obtain the "best" constants occurring in some of these results (n = 2). The proofs depend on the technique introduced in [5] for discussing asymptotic behavior of solutions of perturbed linear systems with constant coefficients (cf. [2, Chapter X]). This technique is based on suitable changes of variables and arguments which have been subsumed by general theorems of Wa2ewski [15], (cf. [2, pp. 278-283]). ??l and 2 use the simple Lemma 4.2, [2, p. 285]; ?3 requires a generalization given as Theorem (*) in an Appendix below. In addition to arguments from the theory of asymptotic integration, the proofs use a theorem of Polya [14] characterizing equations (0.1) disconjugate on an open interval I in terms of Wronskians of subsets of solutions of (0.1); for a generalization, see [2, pp. 51-54] (also obtained in [6]). Theorems I** and IV of Polya [14] show that no solution ( 0) of (0. 1) on an open interval I has n distinct zeros if and only if no solution (X0) has n zeros counting multiplicities; cf. also [13]. (A generalization of this last fact, when the linear family of solutions of (0.1) is replaced by an arbitrary (not necessarily linear) interpolating family of functions, is given in [1].) In ?4, it is observed that the results of the previous sections, together with theorems and methods of Lasota and Opial [8], give criteria for the existence of solutions of certain nonlinear boundary value problems.