A measurement of the cross section for the production of top quark-antiquark pairs (t\overline{t}) in association with a vector boson V (W or Z) in proton-proton collisions at (\sqrt{s})=8TeV is presented. The results are based on a dataset corresponding to an integrated luminosity of 19.5 fb⁻¹ recorded with the CMS detector at the LHC. The measurement is performed in three leptonic (e and (\mu)) channels: a same-sign dilepton analysis targeting (t\overline{t}W) events, and trilepton and four-lepton analyses designed for (t\overline{t}Z) events. In the same-sign dilepton channel, the (t\overline{t}W) cross section is measured as(\sigma_{t\overline{t}W} = 170_{-90}^{+90} (stat) ± 70 (syst) fb), corresponding to a significance of 1.6 standard deviations over the background-only hypothesis. Combining the trilepton and four-lepton channels, a direct measurement of the (t\overline{t}Z) cross section, (\sigma_{t\overline{t}Z} = 200_{-70}^{+80} (stat)_{-30}^{+40} (syst)fb^{-1}), is obtained with a significance of 3.1 standard deviations. The measured cross sections are compatible with standard model predictions within their experimental uncertainties. The inclusive (t\overline{t}V) process is observed with a significance of 3.7 standard deviations from the combination of all three leptonic channels.