A new approach for assessing nonlinear interaction effects and closed-loop nonlinearity in multivariable processes is presented. It is based on a differential geometric interpretation of the relative gain away that leads naturally to systematic procedures for describing interaction effects of higher order and for assessing closed-loop nonlinearity effects in nonlinear processes. Two types of nonlinear effects associated with the behavior of a process are introduced. Between-channel nonlinearity is associated with the nonlinear dependence of an output channel on other input-output pairings. Within channel nonlinearity is used to identify the nonlinear effects that result from the inherent nonlinearity of an individual output channel. A root-mean-squared measure of nonlinearity is introduced and is used to evaluate the significance of local nonlinear effects. Nonlinear interaction measures are derived that provide tools for assessing input-output pairings in a nonlinear process. This new approach extends the standard techniques and provides an estimate of the effect of nonlinearity on closed-loop interactions.