This article concerns general multivariable nonlinear processes, particularly those with singular characteristic matrix. A precise characterization of the structural process properties that give rise to generic singularity of the characteristic matrix is initially developed within a graph-theoretic analysis framework. An output feedback controller synthesis problem is then formulated for multivariable processes with singular characteristic matrix. A comprehensive solution to this problem is obtained through a combination of dynamic state feedback controllers and state observers. The performance and robustness characteristics of the proposed control methodology are illustrated through simulations in a double-effect evaporator.