We first obtain sufficiency conditions for the oscillation of all solutions of linear partial difference equation a A m + 1 , n + 1 + b A m + 1 , n + c A m , n + 1 − d A m , n + P m , n A m − k , n − 1 = 0 . Next, we establish a linearized oscillation result for the nonlinear partial difference equation A m + 1 , n + 1 + A m + 1 , n + A m , n + 1 − A m , n + P m , n f ( A m − k , n − l ) = 0 .