We investigate the asymptotic behavior of solutions to the following system of second order nonhomogeneous difference equation: { u n + 1 − ( 1 + θ n ) u n + θ n u n − 1 ∈ c n A u n + f n n ≥ 1 u 0 = x , sup n ≥ 0 | u n | < + ∞ where A is a maximal monotone operator in a real Hilbert space H , { c n } and { θ n } are positive real sequences and { f n } is a sequence in H . We show the weak and strong convergence of solutions and their weighted averages to an element of A − 1 ( 0 ) , which is the asymptotic center of the sequence { u n } , under appropriate assumptions on the sequences { c n } , { θ n } and { f n } . Our results continue our previous work in Djafari Rouhani and Khatibzadeh (2008, 2010) [30,31], by presenting some new results on the asymptotic behavior of solutions, including in particular a completely new strong convergence result, and extend some previous results by Apreutesei (2003) [27,28], Morosanu (1979) [21] and Mitidieri and Morosanu (1985–86) [22] to the nonhomogeneous case and without assuming A to have a nonempty zero set.