  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
KK-quarks 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 picobarns for the lightest resonances. Two body decays
of the constituent KK-quarks lead to distinctive experimental signatures.
