The invention relates to non-metallocene catalyst systems useful for preparing olefin homopolymers or copolymers. The catalyst systems comprise a cocatalyst and a Group 3-10 transition metal compound that incorporates a diimine ligand in which sp.sup.2-hybridized carbons of the imine groups are joined by a specific divalent one- or two-membered bridge (Y) comprising nitrogen and/or oxygen. The invention includes the diimine ligands, the transition metal compounds, the catalyst systems, and processes for making the ligands, transition metal compounds, catalyst systems, and olefin homopolymers or copolymers. ##STR00001##