One of the main reasons why nonlinear-optical signal processing (regeneration, logic, etc.) has not yet become a practical alternative to electronic processing is that the all-optical elements with nonlinear input–output relationship have remained inherently single-channel devices (just like their electronic counterparts) and, hence, cannot fully utilise the parallel processing potential of optical fibres and amplifiers. The nonlinear input–output transfer function requires strong optical nonlinearity, e.g. self-phase modulation, which, for fundamental reasons, is always accompanied by cross-phase modulation and four-wave mixing. In processing multiple wavelength-division-multiplexing channels, large cross-phase modulation and four-wave mixing crosstalks among the channels destroy signal quality. Here we describe a solution to this problem: an optical signal processor employing a group-delay-managed nonlinear medium where strong self-phase modulation is achieved without such nonlinear crosstalk. We demonstrate, for the first time to our knowledge, simultaneous all-optical regeneration of up to 16 wavelength-division-multiplexing channels by one device. This multi-channel concept can be extended to other nonlinear-optical processing schemes.