The authors consider the first order nonlinear neutral delay differential equation (E) [y(t) + P(t) y(t − τ)]′ − Q(t) ƒ(y(t − σ)) = 0, where P, Q, and ƒ are continuous, Q(t) 0, τ 0, σ 0, and uƒ(u) > 0 if u ≠ 0. They give sufficient conditions for all nonoscillatory solutions of (E) to converge to zero as t → ∞. Two oscillation theorems for equation (E) are also proved.