A search for new long-lived particles decaying to leptons using proton–proton collision data produced by the CERN LHC at √s=13TeV is presented. Events are selected with two leptons (an electron and a muon, two electrons, or two muons) that both have transverse impact parameter values between 0.01 and 10cm and are not required to form a common vertex. Data used for the analysis were collected with the CMS detector in 2016, 2017, and 2018, and correspond to an integrated luminosity of 118 (113)fb⁻¹ in the ee channel (eμ and μμ channels). The search is designed to be sensitive to a wide range of models with displaced eμ, ee, and μμ final states. The results constrain several well-motivated models involving new long-lived particles that decay to displaced leptons. For some areas of the available phase space, these are the most stringent constraints to date.