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 fb−1. The measurements are performed in the lepton + jets decay channels (e + jets and μ + jets) and the dilepton decay channels (e+e−, μ+μ−, and μ±e∓). The tt¯ 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 tt¯ 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.