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A multivariate structured total least squares problem is considered, in which the extended data matrix is partitioned into blocks and each of the blocks is Toeplitz/Hankel structured, unstructured, or noise free. Two types of numerical solution methods for this problem are proposed: (i) standard local optimization methods in combination with efficient evaluation of the cost function and its first derivative, and (ii) an iterative procedure proposed originally for the element‐wise weighted total least squares problem. The computational efficiency of the proposed methods is compared with this of alternative methods. Copyright © 2004 John Wiley & Sons, Ltd.