We obtain a set of sufficient conditions under which all positive solutions of the nonlinear delay difference equation x n + 1 = x n f ( x n − k ) , n = 0 , 1 , 2 , … {x_{n + 1}} = {x_n}f({x_{n - k}}),n = 0,1,2, \ldots , are attracted to the positive equilibrium of the equation. Our result applies, for example, to the delay logistic model N t + 1 = α N t / ( 1 + β N t − k ) {N_{t + 1}} = \alpha {N_t}/(1 + \beta {N_{t - k}}) and to the delay difference equation x n + 1 = x n e r ( 1 − x n − k ) {x_{n + 1}} = {x_n}{e^{r(1 - {x_{n - k}})}} .