Recent empirical research by Mark Taylor and co-authors has found evidence of hybrid dynamics for the real exchange rate. While there is a random walk near equilibrium, for real exchange rates some distance from equilibrium there is mean-reversion which increases with the degree of misalignment. An interesting question is whether this nonlinear mean-reversion is policy-induced. John Williamson (1998), for example, has proposed a "monitoring band" in which there is no intervention near equilibrium but there is substantial intervention triggered by exchange rate deviations outside a preset band. In this paper we develop a theoretical model for a stylised monitoring band to see whether it can generate patterns of nonlinear mean-reversion akin to those reported in empirical research