A sensitivity analysis for the new generation of fast reactors [Salvatores (2008)] has shown the importance of improved cross section data for several actinides. Among them, the240,242Pu(n,f) cross sections require an accuracy improvement to 1-3% and 3-5%, respectively, from the current level of 6% and 20%. At the Van de Graaff facility of the Institute for Reference Materials and Measurements (JRC-IRMM) the fission cross section of the two isotopes was measured relative to two secondary standard reactions,237Np(n,f) and238U(n,f), using a twin Frisch-grid ionization chamber. The secondary standard reactions were benchmarked through measurements against the primary standard reaction235U(n,f) in the same geometry. Sample masses were determined by means of low-geometry alpha counting or/and a 2p Frisch-grid ionization chamber, with an uncertainty lower than 2%. The neutron flux and the impact of scattering from material between source and target was examined, the largest effect having been found in cross section ratio measurements between a fissile and a fertile isotope. Our240,242Pu(n,f) cross sections are in agreement with previous experimental results and slightly lower than present evaluations. In case of the242Pu(n,f) reaction no evidence for a resonance at En=1.1 MeV was found.