Theoretical results for the output and the input-output crosscorrelation function are derived for first order direction-dependent processes perturbed using pseudo-random maximum length ternary (MLT) signals with unsymmetrical signal levels. The analytical results are valid if the process output is either always increasing or always decreasing when the input is at its median level of zero. It is shown that, although this is not normally the case for the whole of the signal period, good approximations to the analytical results are obtained when it is the case for most of the signal period, as can be achieved with a suitable choice of signal levels. MLT signals with unequal spacing between signal levels can also be used to minimise the nonlinear distortion. This is equivalent to compensating for the direction-dependent behaviour of the system by preceding it with a static nonlinearity. Based on the theoretical and simulation results obtained, a novel technique is proposed to allow the best linear approximation of the process to be estimated from the ratio between the amount of time when the output increases to that when it decreases. The proposed method is shown to be applicable even when the number of signal levels is greater than three, and is less susceptible to the effects of noise than the method of correlation analysis and least squares. (C) 2003 Elsevier Ltd. All rights reserved.