A search for the electroweak production of supersymmetric particles in protonproton collisions at a center-of-mass energy of 13TeV is presented in final states with a tau lepton pair. Both hadronic and leptonic decay modes are considered for the tau leptons. Scenarios involving the direct pair production of tau sleptons, or their indirect production via the decays of charginos and neutralinos, are investigated. The data correspond to an integrated luminosity of 35: 9 fb collected with the CMS detector in 2016. The observed number of events is consistent with the standard model background expectation. The results are interpreted as upper limits on the cross section for tau slepton pair production in di ff erent scenarios. The strongest limits are observed in the scenario of a purely left-handed low mass tau slepton decaying to a nearly massless neutralino. Exclusion limits are also set in the context of simpli fi ed models of chargino-neutralino and chargino pair production with decays to tau leptons, and range up to 710 and 630 GeV, respectively.