Some new results are obtained for the bounded and monotone properties of solutions of second-order quasi-linear forced difference equations Δ(pn-1(Δyn-1)α) = q nynβ + rn, n ≥n 0, where n0 ∈N = {0, 1, 2, 3,... }, {p n}n=n0-1∞ is a positive sequence, {q n}n=n0∞ is a nonnegative real sequence with qn ≢0, {rn}n=n0∞ is a real sequence, and αand βare quotients of odd positive integers. Some errors in [1] are pointed out and addressed. Examples are given to illustrate the advantages of the new results. ©2004 Elsevier Ltd. All rig...