Leptoquarks can be produced in pairs by gluon-gluon fusion and quark-a
ntiquark annihilation at hadron colliders. While HERA is the proper ma
chine for single production of (eu) and (ed) type leptoquarks, the fla
vor species of (muu), (mud) and (tauu), (taud) type leptoquarks can be
produced at hadron colliders very efficiently. Besides exploiting glu
on-quark collisions, leptoquarks can also be produced singly by collid
ing the quarks in one proton beam with leptons e, mu, tau generated by
splitting photons which are radiated off the quarks in the other prot
on beam. For Yukawa couplings of the size alpha leptoquark masses up t
o about 300 GeV can be generated at the Tevatron while the LHC can pro
duce leptoquarks with masses up to about 3 TeV. [Leptoquarks involving
heavy quarks can be produced singly at a lower rate, determined by th
e heavy flavor flux in the proton beam.]