In this paper we study the oscillation of the difference equations of the form Δ 2 xn+PnΔxn + f(n, Xn-ff, Δx n-h) = 0, in comparison with certain difference equations of order one whose oscillatory character is known. The results can be applied to the difference equation Δ 2 xn+pnΔxn +q n |x-_g|λ|Δxn -h |μ sgnx„-9 = 0, where A and \i are real constants, λ > 0 and μ ≥ 0.
Various new criteria for the oscillation of nonlinear neutral difference equations of the form Δi (xn — x n - h) + qn\xn~g\c sgns n -9 =0 , i = 1,2,3 and c > 0, are established.