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In many adaptive control applications an accurate model identification process has to be performed in almost every timing instant in which new plant data are monitored. Such an accurate identification process can be based on well trained recurrent neural networks. In this work a new adaptive recurrent neural network training algorithm (ARNNTA) based on supervised learning with a new trust region strategy is developed. The ARNNTA is applied to two highly multivariable nonlinear systems that is, a wastewater treatment plant and the F-16 fighter aircraft. Comparison of model validation results with the back propagation and recursive incremental back-propagation algorithms show the superiority of the ARNNTA.