We obtain a necessary and sufficient condition for the oscillation of all solutions of the neutral delay differential equation: (1) \[ d d t [ x ( t ) + p x ( t − τ ) ] + Q ( t ) x ( t − σ ) = 0 , \tfrac {d}{{dt}}[x(t) + px(t - \tau )] + Q(t)x(t - \sigma ) = 0, \] where p ∈ R , Q ∈ C [ [ 0 , ∞ ) , R + ] , Q p \in {\mathbf {R}},Q \in C[[0,\infty ),{{\mathbf {R}}^ + }],Q is ω \omega -periodic with ω > 0 , Q ( t ) [ u n k ] 0 \omega > 0,Q(t)[unk]0 for t ≧ 0 t \geqq 0 , and there exist positive integers n 1 {n_1} and n 2 {n_2} such that τ = n 1 ω \tau = {n_1}\omega and σ = n 2 ω \sigma = {n_2}\omega . More precisely we show that every solution of (1) oscillates if and only if every solution of an associated neutral equation with constant coefficients oscillates.