An important generalisation of the state dependent parameter approach to the modelling of nonlinear dynamic systems to include multi-state dependent parameter (MSDP) nonlinearities is described. The recursive estimation of the MSDP model parameters in a multivariable state space occurs along a multipath trajectory, employing the Kalman filter and fixed interval smoothing algorithms. The novelty of the method lies in redefining the concepts of sequence (predecessor, successor), allowing for its use in a multi-state dependent context, so producing efficient parameterisation for a fairly wide class of nonlinear, stochastic dynamic systems. The format of the estimated model allows its direct use in control system design.