The parabolic partial difference equation is considered which is nonlinear and of neutral type \[ \triangle_2(y_{m,n} - p_ny_{m,n-r}) + \sum_{i\in{\mathcal I}}q^{(i)}_{m,n}f(y_{m,n-\sigma_i}) = r_n\nabla^2y_{m-1,n+1} + \sum_{j\in{\mathcal J}}R_{j,n}\nabla^2y_{m-1,n+1-\gamma_j} \] with \({\mathcal I}, {\mathcal J}\) two sets of indices, \(\{y_{m,n}\} = \{y_{m_1,m_2,\dots,m_l,n}\}\), \(\nabla^2\) is the discrete Laplacian operator and \(\triangle_i^2\) is a partial difference operator of order 2; \(i\) denotes the argument with respect to which the difference is performed. Two kinds of boundary conditions are considered \[ \triangle_Ny_{m-1,n} = 0,\quad\text{on }\partial\Omega\times{\mathbb N}_{n_0} \] and \[ \triangle_Ny_{m-1,n} + g_{m,n}y_{m,n} = 0,\quad \text{on }\partial\Omega\times{\mathbb N}_{n_0} \] \(\Omega\) being the set of the ``space'' arguments denoted by \(\{m_1,\dots,m_l\}\) and \(\triangle_N\) the normal difference on the boundary of \(\Omega\). The author proves oscillation conditions for the solutions of the two boundary value problems.