It is shown that electron-positron pair production is expected to occur in post-disruption plasmas in large tokamaks, including JET and JT-60U, where up to about 10 14 positrons may be created in collisions between multi-MeV runaway electrons and thermal particles. If the loop voltage is large enough, they are accelerated and form a beam of long-lived runaway positrons in the direction opposite to that of the electrons; if the loop voltage is smaller, the positrons have a lifetime of a few hundred ms, in which they are slowed down to energies comparable to that of the cool ( = 10 eV ) background plasma before being annihilated.