The normalized differential cross section for top quark pair (tt¯) production is measured in pp collisions at a centre-of-mass energy of 8TeV at the CERN LHC using the CMS detector in data corresponding to an integrated luminosity of 19.7fb-1. The measurements are performed in the lepton+jets (e/μ++jets) and in the dilepton e+e-, μ+μ-, and e±μ∓) decay channels. The tt¯ cross section is measured as a function of the kinematic properties of the charged leptons, the jets associated to b quarks, the top quarks, and the tt¯ system. The data are compared with several predictions from perturbative quantum chromodynamic up to approximate next-to-next-to-leading-order precision. No significant deviations are observed relative to the standard model predictions.