A geometric derivation of nonholonomic integrators is developed. It is based in the classical technique of generating functions adapted to the special features of nonholonomic systems. The theoretical methodology and the integrators obtained are, in general, different from the previously obtained.This work has been supported by grant BFM2001-2272. A. Santamaría Merino wishes to thank the Programa de formación de Investigadores of the Departamento de Educación, Universidades e Investigación of the Basque Government (Spain) for financial support.Peer reviewed