This paper is focused on possible designs and predicted performances of two proposed highenergy, high-luminosity electron-hadron colliders: eRHIC at Brookhaven National Laboratory (BNL, Upton, NY, USA) and LHeC at Organisation Européenne pour la Recherche Nucléaire (CERN, Geneve, Switzerland). The Relativistic Heavy Ion Collider (RHIC, BNL) and the Large Hadron Collider (LHC, CERN) are designed as versatile colliders. RHIC is colliding various species of hadrons staring from polarized protons to un-polarized heavy ions (such as fully stripped Au (gold) ions) in various combinations: polarized p-p, d-Au, Cu-Cu, Au-Au. Maximum energy in RHIC is 250 GeV (per beam) for polarized protons and 100 GeV/n for heavy ions. There is planed expansion of the variety of species to include polarized He3 and unpolarized fully stripped U (uranium). LHeC is designed to collide both un-polarized protons with energy up to 7 TeV per beam and fully stripped Pb (lead) ions with energy up to 3 TeV/n. Both eRHIC and LHeC plan to add polarized electrons (or/and positrons) to the list of colliding species in these versatile hadron colliders. In eRHIC 10-20 GeV electrons would collide with hadrons circulating in RHIC. In LHeC 50-150 GeV polarized leptons will collided with LHC’s hadron beams. Both colliders plan to operate in electron-proton (in RHIC case protons are polarized as well) and electron-ion collider modes. eRHIC and LHeC colliders are complimentary both in the energy reach and in their physics goals. I will discuss in this paper possible choices of the accelerator technology for the electron part of the collider for both eRHIC and LHeC, and will present predicted performance for the colliders. In addition, possible staging scenarios for these colliders will be discussed