Nonminimum-phase (NMP) processes are frequently encountered in chemical plants, where the presence of right half-plane zeros and time delays often imposes limitations on the achievable control performance. In this article, a new multiscale control scheme for controlling NMP processes is introduced. The novelty of the proposed scheme is to decompose a given plant into a sum of basic factors/modes having distinct speeds of responses. Then, an individual subcontroller is specifically designed to control each of these plant modes. Finally, an overall multiscale controller is synthesized by combining all of the subcontrollers in a way that enhances good cooperation among the different modes, which is an essential feature for good control performance and robustness. Extensive numerical studies demonstrate that the proposed scheme can provide better nominal performance and performance robustness than some well-established control schemes.