Necessary and sufficient conditions are obtained for oscillation of all bounded solutions of (∗) [y(t) − y(t − τ )](n) + Q(t)G(y(t − σ)) = 0, t ≥ 0, where n ≥ 3 is odd. Sufficient conditions are obtained for all solutions of (∗) to oscillate. Further, sufficient conditions are given for all solutions of the forced equation associated with (∗) to oscillate or tend to zero as t → ∞. In this case, there is no restriction on n.