Consider the second-order quasilinear neutral difference equation (*) Δ a n|Δ(x n+p nx g(n))| α−1Δ(x n+p nx g(n)) +f(n,x σ(n))=0. The sufficient conditions are established for oscillation of the solution of this Eq. (*). These generalize and improve some known results about both neutral and delay difference equations.