The identification of linear systems with unknown orders is considered. The observed input and output signals are corrupted by the Gaussian random coloured noise or other non-Gaussian random coloured noise with zero third-order statistics. It is also assumed that a priori statistical information of these two kinds of noise (input and output) is unknown. The input signal to the identified system is a zero-mean, stationary non-Gaussian random sequence. By applying a proposed estimation algorithm, the system orders and parameters can be estimated accurately. Finally, two simulation results are presented to illustrate the proposed algorithm.