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Empirical modelling in high dimensional spaces is usually preceded by a feature selection stage. Irrelevant or noisy features unnecessarily increase the complexity of the problem and can degrade modelling performance. Here, multiobjective genetic algorithms are proposed as effective means of evolving a diverse population of alternative feature sets with various accuracy/complexity trade-offs. They are shown to be particularly successful in neurofuzzy modelling, in conjunction with a method for performing fast fitness evaluation. The major contributions of the paper are in the use of a specific type of multiobjective genetic algorithm, based on the concept of dominance, for feature selection; and the combination of fast fitness evaluation of neurofuzzy models with a genetic algorithm. The effectiveness of the proposed approach is demonstrated on two high-dimensional regression problems.