Consider the forced nonlinear difference equation \(\Delta [y_ n + p_ n y_{n-h}] + q_ n f(y_{n-k}) = r_ n\) where \(h,k \in \{0,1, \dots\}\) and \(f : \mathbb{R} \to \mathbb{R}\) is continuous with \(uf(u) > 0\) for \(u \neq 0\). The authors present conditions which are sufficient for nonoscillatory or so-called \(Z\)-type solutions to be bounded or converge to zero. Examples illustrating the results are also included.