Chemical processes with input multiplicity behavior place a limitation on the structure of the feedback controller. Systems with right-half-plane zeroes (characteristic inverse response) also pose inherent feedback performance limitations. In this paper we prove that systems with input multiplicity must, under some assumptions, have right-half-plane zeroes on one "side" of the steady-state operating curve. A discrete dynamic model of a system with input multiplicity is shown to exhibit nonminimum-phase behavior. Stabilizing tuning parameters (prediction horizon and weighting on the inputs) for unconstrained nonlinear predictive control of nonlinear processes are found using the convergence theory of iterative processes. Closed-loop regions of attraction are constructed using a numerical Lyapunov function. Stabilization using nonlinear predictive control and significance of the closed-loop region of attraction are demonstrated on the isothermal Van de Vusse reaction and on the classic irreversible adiabatic CSTR.