Stop particles are expected to be the lightest squarks in supersymmetr
ic theories and the search for these particles is an important experim
ental task. We therefore present the cross sections for the production
processes p (p) over bar/pp --> (t) over tilde(1) (t) over tilde(1) a
nd (t) over tilde(2) (t) over tilde(2) at Tevatron and LHC energies in
next-to-leading order supersymmetric QCD. The corrections stabilize t
he theoretical predictions for the cross sections, and they are positi
ve, thus raising the cross sections to values above the leading-order
predictions. Mixed (t) over tilde(1) (t) over tilde(2)/(t) over tilde(
1) (t) over tilde(2) pairs can only be generated in higher orders at s
trongly suppressed rates. (C) 1998 Elsevier Science B.V.