In this paper, a unified review of eight decomposition methods is presented. A two-level decomposition method is proposed, which is an extension of feasible model coordination methods. The method couples the global monotonicity analysis of the first- level subproblem(s) with an optimization method (single-level method) of the second-level. Three classes of problems are considered where in the first-level they have (1) one subproblem with one local variable, (2) several subproblems with one local variable, and (3) several subproblems with several local variables. Some test results have been presented which show the substantially improved performance of the proposed approach over a single-level optimization method.