A search is presented for τ slepton pairs produced in proton–proton collisions at a center-of-mass energy of 13. The search is carried out in events containing two τ leptons in the final state, on the assumption that each τ slepton decays primarily to a τ lepton and a neutralino. Events are considered in which each τ lepton decays to one or more hadrons and a neutrino, or in which one of the τ leptons decays instead to an electron or a muon and two neutrinos. The data, collected with the CMS detector in 2016 and 2017, correspond to an integrated luminosity of 77.2. The observed data are consistent with the standard model background expectation. The results are used to set 95% confidence level upper limits on the cross section for τ slepton pair production in various models for τ slepton masses between 90 and 200 and neutralino masses of 1, 10, and 20. In the case of purely left-handed τ slepton production and decay to a τ lepton and a neutralino with a mass of 1, the strongest limit is obtained for a τ slepton mass of 125 at a factor of 1.14 larger than the theoretical cross section.