A generalised H-infinity controller for nonlinear multivariable systems is derived. This is a development of a special form of the nonlinear generalised minimum variance (NGMV) controller (the so-called factorised form). The system is modelled as a combination of a linear and a nonlinear subsystem, where the plant can have severe non-smooth nonlinearities but the disturbance and reference models are assumed linear. The H-infinity cost-function to be penalised involves both error and control signal costing terms, which are related to the sensitivity and control sensitivity functions. The H-infinity criterion enables these sensitivity functions to be frequency shaped to modify and improve robust properties. The nonlinear generalised H-infinity (NGH(infinity)) controller is a development of the so-called factorised NGMV controller, where the cost-function weightings satisfy a particular relationship. A lemma is derived which provides a link between the factorised NGMV and the proposed NGH(infinity) control problem. This involves a linking dynamic cost-function weighting that relates the two types of optimisation problem. The controller obtained is simple to implement and includes an internal model of the process. Like the family of NGMV controllers, it may be related to a nonlinear version of the Smith predictor, which is helpful in providing some confidence in the solution. However, unlike the Smith predictor, a stabilising control law can be obtained even for some open-loop unstable processes. The main benefit of the approach is that the controller is straightforward to implement.