Some new criteria for the oscillation of third order nonlinear neutral difference equations of the form ∆(an(∆2 (xn + bnxn−δ))α ) + qnx α n+1−τ = 0 and ∆(an(∆2 (xn − bnxn−δ))α ) + qnx α n+1−τ = 0 are established. Some examples are presented to illustrate the main results.