We study the bounds states of the Kaluza-Klein (KK) excitations of quarks in models of Universal Extra Dimensions. Such bound states may be detected at future lepton colliders in the cross section for the pair-production of KKquarks near threshold. For typical values of model parameters, we find the “KK-quarkonia” have widths in the 10-100 MeV range, and production cross sections of order a few...