For a delay difference equation N ( n + 1 ) − N ( n ) = N ( n ) ∑ k = 1 m a k ( n ) ( 1 − N ( g k ( n ) ) / K ) , a k ( n ) ≥ 0 , g k ( n ) ≤ n , K > 0 , a connection between oscillation properties of this equation and the corresponding linear equations is established. Explicit nonoscillation and oscillation conditions are presented. Positiveness of solutions is discussed.