Model selection is concerned with the choice of a mathematical model from a set of candidates that best describes a given set of experimental data. Large families of models arise in the context of structured mechanistic modelling in several application fields. In this situation the model selection problem cannot be solved by brute force testing of all possible models because of the high computational costs. However, more information on the different models of a family is available by their interdependencies, given by generalization or simplification relations. Large-scale model selection algorithms should exploit these relations for navigation in the discrete space of all model candidates. This paper presents a general approach for large-scale model selection by specifying the necessary computational primitives for navigating in large model families. As a non-trivial example it is shown how families of biochemical network models arising from the evaluation of stimulus response experiments are mapped to the general formalism. Finally, a first model selection algorithm based on the mentioned computational primitives is introduced and applied to complex biochemical network experiments. It is based on a load-balancing algorithm by making use of grid computing facilities.