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Some new criteria for the oscillation of third order nonlinear neutral difference equations of the form $$\Delta \left(a_n{\left({\Delta }^2(x_n+b_n{x}_{n-\delta })\right)}^{\alpha }\right)+q_n{x}_{n+1-\tau }^{\alpha }=0$$ and $$\Delta \left(a_n{\left({\Delta }^2(x_n-b_n{x}_{n-\delta })\right)}^{\alpha }\right)+q_n{x}_{n+1-\tau }^{\alpha }=0$$ are established. Some examples are presented to illustrate the main results.