Consider the even-order neutral difference equation (*) ${delta}^m(x_n{-}p_ng(x_{n-k}))-q_nh(x_{n-1})=0$, n=0,1,2,... where $Delta$ is the forward difference operator, m is even, ${-p_n},{q_n}$ are sequences of nonnegative real numbers, k, l are nonnegative integers, g(x), h(x) ${in}$ C(R, R) with xg(x) > 0 for $x;{ eq};0$. In this paper, we obtain some linearized oscillation theorems of (*) for $p_n;{in};(-{infty},0)$ which are discrete results of the open problem by Gyori and Ladas.