This article introduces two Tensor Network-based iterative algorithms for the identification of high order discrete-time nonlinear multiple-input multiple-output (MIMO) Volterra systems. The system identification problem is rewritten in terms of a Volterra tensor, which is never explicitly constructed, thus avoiding the curse of dimensionality. It is shown how each iteration of the two identification algorithms involves solving a linear system of low computational complexity. The proposed algorithms are guaranteed to monotonically converge and numerical stability is ensured through the use of orthogonal matrix factorizations. The performance and accuracy of the two identification algorithms are illustrated by numerical experiments, where accurate degree-10 MIMO Volterra models are identified in about 1 s using Matlab on a 3.3 GHz quad-core desktop computer with 16 GB RAM. (C) 2017 Elsevier Ltd. All rights reserved.