The authors consider the third order nonlinear delay difference equations \[ x_{n+1}=f(x_n,x_{n-1},x_{n-2}). \] They study the oscillation behavior of the solutions and the lengths of the semicycles. The results are applied to the nonlinear delay difference equation \[ x_{n+1}=\frac{a+x_n^b}{x_{n-1}^s x_{n-1}^q} \] and some sufficient conditions for oscillation of all solutions about the positive steady state are established.