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This paper presents a multiobjective learning algorithm for the random neural network RNN. A learning process consists in updating the parameters of the RNN. In a monoobjective approach, this update is made by means of the minimisation of one objective function, which is usually quadratic error of input-output. Here, we state a general procedure to update the parameters that take into account more than one objective. The parameter estimation is described as a multiobjective optimisation problem MOP and it is solved using weighting problem and gradient descent. The solution of MOP is a set called Pareto-set. A case study is presented, where quadratic error of dynamic input-output and the quadratic error of static curve were used to estimate the parameters of the RNN. We show that multiobjective learning improves the quality of models built from limited-range dynamic data.