The normalized differential cross section for top quark pair ( tt¯tt¯ ) production is measured in pp collisions at a centre-of-mass energy of 8 TeVTeV at the CERN LHC using the CMS detector in data corresponding to an integrated luminosity of 19.7 fb−1fb−1 . The measurements are performed in the lepton ++ jets ( e/μe/μ ++ jets) and in the dilepton ( e+e−e+e− , μ+μ−μ+μ− , and e±μ∓e±μ∓ ) decay channels. The tt¯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¯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.