The use of finite-state model-predictive controllers for current control of multi-phase machines is investigated. The basic setup is comprised a predictive model and an exhaustive optimizer that minimizes a predefined cost function for the next sampling period. The output of the predictive controller is a vector of gating signals to be applied to a voltage source inverter. The inverter can accommodate just a finite number of configurations and hence the name of finite-state. The use of predictive controllers, already proposed for three-phase drives, is applied here to multi-phase drives. Some implementation issues are discussed along, including the choice of the cost function, the switching frequencies applied to the inverter and the computation time needed for optimization. Simulation and experimental results are provided illustrating various aspects of the control scheme using an asymmetrical dual three-phase AC motor drive as a test bed.