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<p>Abstract</p> <p>A new system of nonlinear variational inclusions involving <inline-formula> <graphic file="1029-242X-2008-681734-i2.gif"/></inline-formula>-monotone mappings in the framework of Hilbert space is introduced and then based on the generalized resolvent operator technique associated with <inline-formula> <graphic file="1029-242X-2008-681734-i3.gif"/></inline-formula>-monotonicity, the approximation solvability of solutions using an iterative algorithm is investigated. Since <inline-formula> <graphic file="1029-242X-2008-681734-i4.gif"/></inline-formula>-monotonicity generalizes <inline-formula> <graphic file="1029-242X-2008-681734-i5.gif"/></inline-formula>-monotonicity and <inline-formula> <graphic file="1029-242X-2008-681734-i6.gif"/></inline-formula>-monotonicity, our results improve and extend the recent ones announced by many others.</p>