Results are presented from a search for the electroweak production of supersymmetric particles in pp collisions in final states with two T leptons. The data sample corresponds to an integrated luminosity between 18.1 fb(-1) and 19.6 fb(-1) depending on the final state of T lepton decays, at root s = 8 TeV, collected by the CMS experiment at the LHC. The observed event yields in the signal regions are consistent with the expected standard model backgrounds. The results are interpreted using simplified models describing the pair production and decays of charginos or T sleptons. For models describing the pair production of the lightest chargino, exclusion regions are obtained in the plane of chargino mass vs. neutralino mass under the following assumptions: the chargino decays into third-generation sleptons, which are taken to be the lightest sleptons, and the sleptons masses lie midway between those of the chargino and the neutralino. Chargino masses below 420 GeV are excluded at a 95% confidence level in the limit of a massless neutralino, and for neutralino masses up to 100 GeV, chargino masses up to 325 GeV are excluded at 95% confidence level. Constraints are also placed on the cross section for pair production of T sleptons as a function of mass, assuming a massless neutralino.