The spectra of strange hadrons are measured in proton-proton collisions, recorded by the CMS experiment at the CERN LHC, at centre-of-mass energies of 0.9 and 7TeV. The K0 S, Lambda, and - particles and their antiparticles are reconstructed from their decay topologies and the production rates are measured as functions of rapidity and transverse momentum, p T. The results are compared to other experiments and to predictions of the Pythia Monte Carlo program. The pT distributions are found to differ substantially from the Pythia results and the production rates exceed the predictions by up to a factor of three. © SISSA 2011.