  I discuss the production of leptoquarks in $p\bar{p}$ collisions at the
Fermilab Tevatron. Evaluated on the basis of a recent next-to-leading order
calculation, the combined D0 and CDF leptoquark searches lead to a
parameter-free lower mass bound of about $\ms \simgt 240$ GeV for scalar
leptoquarks or squarks decaying solely to a first generation charged lepton
plus quark. These results provide very stringent constraints on any explanation
of the recently observed HERA excess events in terms of new particle
production.
