Direction-dependent dynamic systems are defined, and Wiener models for them are described. For first-order systems with pseudo-random binary inputs, optimising the model parameters by cross-correlation function matching methods based on analysis gives excellent results. For first-order systems with inverse-repeat pseudo-random binary inputs, optimisation by discrete Fourier transform matching and output matching methods also give excellent results. These optimisation methods may be extended to direction-dependent dynamic systems that cannot be analysed, as illustrated by a first-order system with a pseudo-random ternary input, and a second-order system with an inverse-repeat pseudo-random binary input.