We calculate flavor-changing neutral-current (FCNC) processes involving top-quark production via anomalous tqV couplings at the Tevatron and HERA colliders. We cover the FCNC processes p¯p → tZ, p¯p → t , p¯p → tt, and ep → et. We go beyond leading order and include the effects of soft-gluon corrections through next-to-next-to-leading order. We demonstrate the stabilisation of the cross section with respect to the variation of QCD scale, and we investigate the reach of the Tevatron and HERA colliders.