By combining the coupling identification concept with the gradient search, this study develops a partially coupled generalised extended projection algorithm and a partially coupled generalised extended stochastic gradient algorithm to estimate the parameters of a multivariable output‐error‐like system with autoregressive moving average noise from input–output data. The key is to divide the identification model into several submodels based on the hierarchical identification principle and to establish the parameter estimation algorithm by using the coupled relationship between these submodels. The simulation test results indicate that the proposed algorithms are effective.