The authors consider the nonlinear difference equation Δ [ y n + p n y n − h ] + q n f ( y n − k ) = r n where Δ y n = y n + 1 − y n , { p n } , { q n } , and { r n } are real sequences, and 0$"> u f ( u ) > 0 for u ≠ 0 . Sufficient conditions for boundedness and convergence to zero of certain types of solutions axe given. Examples illustrating the results are also included.