Many processes have dynamic responses which are dependent on the direction in which the response variable is moving. The effects of such nonlinear behaviour on the weighting-function model of the process obtained by crosscorrelation and on the difference-equation model obtained by a generalised least-squares procedure are determined theoretically for a process with 1st-order dynamics perturbed with pseudorandom binary signals. The theory is confirmed by results from a hybrid-computer simulation, and computer-simulated results for processes with 2nd-order dynamics are also presented. Experimental work on two pilot-scale processes with direction-dependent dynamics is reported, and two further examples from the literature are examined.