Possible bound and resonant states of the hypernuclear systems $��nn$ and $����n$ are sought as zeros of the corresponding three-body Jost functions calculated within the framework of the hyperspherical approach with local two-body S-wave potentials describing the $nn$, $��n$, and $����$ interactions. Very wide near-threshold resonances are found for both three-body systems. The positions of these resonances turned out to be sensitive to the choice of the $��n$-potential. Bound $��nn$ and $����n$ states only appear if the two-body potentials are multiplied by a factor of $\sim 1.5$.

12 pages, 5 figures. Acknowledgments are added in the new version