Normalised differential top-quark pair production cross sections are measured in pp collisions at a centre-of-mass energy of 7 TeV at the LHC with the CMS detector using data recorded in 2011 corresponding to an integrated luminosity of 5.0 inverse femtobarns. The measurements are performed in the lepton+jets decay channels (e+jets and mu+jets) and the dilepton decay channels (oppositely charged ee, mu mu, and e mu). The t t-bar differential cross section is measured as a function of kinematic properties of the final-state charged leptons and jets associated to b quarks, as well as those of the top quarks and the t t-bar system. The data are compared with several predictions from perturbative QCD calculations up to approximate next-to-next-to-leading-order precision. No significant deviations from the standard model are observed.