The asymptotic and oscillatory behavior of solutions of mth order damped nonlinear difference equation of the form \[ \Delta (a_n \Delta ^{m-1} y_n) + p_n \Delta ^{m-1} y_n + q_n f(y_{\sigma (n+m-1)}) = 0 \] where $m$ is even, is studied. Examples are included to illustrate the results.