The low-lying spectra of $^8$He and $^{10}$He nuclei were studied in the $^3$H($^6$He,$p$)$^8$He and $^3$H($^8$He,$p$)$^{10}$He transfer reactions. The $0^+$ ground state (g.s.) of $^8$He and excited states, $2^+$ at $3.6-3.9$ MeV and $(1^+)$ at $5.3-5.5$ MeV, were populated with cross sections of 200, 100-250, and 90-125 $mu$b/sr, respectively. Some evidence for $^8$He state at about 7.5 MeV is obtained. We discuss a possible nature of the near-threshold anomaly above 2.14 MeV in $^8$He and relate it to the population of a $1^-$ continuum (soft dipole excitation) with peak value at about 3 MeV. The lowest energy group of events in the $^{10}$He spectrum was observed at $sim 3$ MeV with a cross section of $sim 140$ $mu$b/sr. We argue that this result is possibly consistent with the previously reported observation of $^{10}$He, in that case providing a new g.s. position for $^{10}$He at about 3 MeV.
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