We use two-body potentials derived from a constituent quark cluster model to analyze the bound-state problem of the $��NN$ system. The observables of the two-body subsystems, $NN$ and $��N$, are well reproduced. We do not find $��NN$ bound states, but there are two attractive channels with a resonance close above the three-body threshold. These channels are the $(I,J)=(1,1/2)$ and $(0,1/2)$, their quantum numbers, widths and energy ordering consistent with the recently measured strange tribaryons from the $^{4}{\rm He}(K_{\rm stopped}^{-},N)$ reactions in the KEK PS E471 experiment.

16 pages, 10 figures, 4 tables. Accepted for publication in Phys. Rev. C