In this paper, the authors establish some sufficient conditions for oscillation and nonoscillation of the second order nonlinear neutral delay difference equation Δ^2(x(subscript n)-p(subscript n)x(subscript (n-k))+q(subscript n)ƒ(x(subscript (n-e))=0, n≥n0 where {p(subscript n)} and {q(subscript n)} are non-negative sequences with 0<p(subscript n)≤1, and k and ℓ are positive integers.