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