In this paper, we obtain sufficient conditions for the oscillation of every solution of the difference equation $$x_{n+1}-x_n+sum_{i=1}^{m}p_ix_{n-k_i}+qx_{n-z}=0,;n=0,1,2,{cdots},$$ where $p_i{in}mathbb{R}$, $k_i{in}mathbb{Z}$ for $i=1,2,{cdots},m$ and $z{in}{-1,0}$. Furthermore, we obtain sufficient conditions for the oscillation of all solutions of the equation $${Delta}^rx_n+sum_{i=1}^{m}p_ix_{n-k_i}=0,;n=0,1,2,{cdots},$$ where $p_i{in}mathbb{R}$, $k_i{in}mathbb{Z}$ for $i=1,2,{cdots},m$. The results are given terms of the $p_i$ and the $k_i$ for each $i=1,2,{cdots},m$.