On the Oscillation, the Convergence, and the Boundedness of Solutions for a Neutral Difference Equation In this paper, the oscillation, convergence and boundedness for neutral difference equations $$\Delta(x_n + \delta_nx_{n-\tau}) + \sum_{i = 1}^r\alpha_i(n)F(x_{n-m_i})=0, \quad n = 0, 1, \cdots$$ are investigated. Keywork: Neutral difference equation, oscillation, nonoscillation, convergence, boundedness.