Abstract: | A search has been made for direct production of heavy quarkonium states in more than 3 million hadronic Z 0 decays in the 1991–1994 DELPHI data. Prompt J/ψ, ψ(2S) and Υ candidates have been searched for through their leptonic decay modes using criteria based on the kinematics and decay vertex positions. New upperlimits are set at the 90% confidence level for Br(Z0 → (QQ) X)/Br (Z0 → hadrons) for various strong production mechanisms of J/ψ and Υ these range down to 0.9 × 10?4. The limits are set in the presence of a small excess (~ 1% statistical probability of a background fluctuation) in the sum of candidates from prompt J/ψ, ψ(2S), Υ(1S),Υ(2S) and Υ(3S) relative to the estimated background. |