to be nonoscillatory. In the case of second-order ordinary equations a variety of such criteria are now known; for example, see [ 10-15 1. The development of nonoscillation criteria for functional equations has proven to be a considerably more difficult problem. Moreover, in view of an example recently constructed by Brands [ 11, the type of integrability criteria usually imposed on q(t) in the study of nonoscillation of ordinary equations will not yield nonoscillation for unforced functional equations. In fact, the only known nonoscillation criteria for functional equations are due to Graef et al. 191, Kusano and Onose [16], and Singh [22, 24, 261 for second-order equations, and Graef [B] and Singh [23] for higher order equations. Only the papers of Chen [2], Graef [7], and Staikos and Philos [29] contain such results for higher order nonlinear ordinary equations. The main result in this paper, Theorem 4, gives sufficient conditions for all solutions of Eq. (*) withf(x) sublinear and r(t) f 0 to be nonoscillatory. In order to prove this theorem we first discuss the asymptotic behavior of the oscillatory solutions of (*). In so doing, we are able to generalize recent results of Chiou [6], Graef et al. [9], Kusano and Onose [ 171, and Singh [ 19,21-261. In the last section of the paper we discuss some possible extensions of the theorems presented here.