We prove sufficient conditions for the oscillation of all solutions of a scalar first-order neutral delay differential equation x ˙ ( t ) − c x ˙ ( t − τ ) + ∑ i = 1 n p i x ( t − σ i ) = 0 for all 0 < c < 1 , τ , 0$"> σ i > 0 , and p i ∈ ℝ , i = 1 , 2 , … , n .