  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.
