Consider the following delay difference equation \[ x_{n+1}-x_n+\sum^m_{i=1}p_i(n)X_{n-k_i}=0,\;n=0,1,\dots, \] where \(p_i(n)\geq 0\) for \(n\geq 0\), \(i=1,2, \dots,m\) and \(k_i\) are positive integers. Every solution of this equation is oscillatory if there exists an integer \(l\geq 1\) such that \[ \sum_{n=0 }^\infty \biggl\{p(n) \bigl[(k+1)/k\bigr]^\ell \bigl(p^l(n) \bigr)^{ 1/(k +1)}-1 \biggr\}= \infty. \] Some illustrative examples are included. Some mistakes in the papers by other authors are pointed out.