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We offer sufficient conditions for the oscillation of all solutions of the partial difference equations y(m - 1,n) + β(m,n)y(m, n - 1) -δ(m,n)+ P(m,n,y(m + k,n + l)) = Q(m,n,y(m + k,n + l)) and (y(m - 1,n)+ β(m,n)y(m,n - 1) - δ(m,n)y(m,n) + $$\mathop \Sigma \limits_{i = 1}^\tau $$ Pi(m,ny(m + ki,n + li)) = $$\mathop \Sigma \limits_{i = 1}^\tau $$ Qi(m,n,y9m + ki,n + li)). Several examples which dwell upon the importance of our results are also included.