In this paper, we introduce an iterative method to study oscillatory properties of delay difference equations of the following form ${ abla}_{alpha};[x(t);-;r(t)x(t;-;k)];+;p(t)x(t;-;{ au});-;q(t)x(t;-;{sigma});=;0$, $t;{geq};t_0$, where $t_0;{in};mathbb{R}$, t varies in the real interval ($t_0,;{infty}$), $alpha$ > 0, $kappa$, $ au$, ${sigma};{geq};0$, $r;{in};C;([t_0-{alpha},;{infty}),;mathbb{R}^+$, p, $q;{in};C;([t_0,;{infty}),;mathbb{R}^+)$ and ${ abla}_{alpha}x(t);=;x(t);-;x(t;-;{alpha})$ for $t;{geq};t_0$.