Two algorithms for centering and tolerancing networks are described. Both use first-order sensitivities to characterise network behaviour. Margin sensitivities are introduced as a simple measure of the likelihood that changes in components will cause specifications to be violated, based on first-order sensitivities. This new measure is used as the basis of the two algorithms. The first uses minimax optimisation in a ‘fixed tolerance’ centering procedure, while the second uses a minimum cost formulation of the problem and a scalar minimisation procedure. Examples demonstrate the effectiveness of the methods.