An experimental search for the low-lying 7 H resonance was performed with the 2 H( 8 He, 3 He) 7 H reaction studied at forward center-of-mass angles (6 • -14 • ) with a 42 A MeV 8 He beam. No well-pronounced peak of 7 H was observed; however, the obtained spectrum was found to have a peculiarity at ∼2 MeV above the t + 4n threshold. The data allow us to set a c.m.s. cross section level of ∼30 µb/sr for the low-energy part of the 7 H spectrum. The test reaction 2 H( 12 Be, 3 He) 11 Li, involving the same one-proton (d, 3 He) transfer, was studied simultaneously on a 71 A MeV satellite beam where a cross section of 1 mb/sr was measured for the population of the 11 Li ground state.