[en] We have used the beam-foil quantum beat method to measure the hyperfine structure separations F = 3/2 - 5/2 of the 1snd ₁D states (n = 3 - 8) of ₃He I. We observed the single frequency modulated decay curves of the 1s2p ₁P - 1snd ₁D transitions for times after excitation up to 50 ns, corresponding to 4 to 5 modulation periods. The frequencies obtained (with a precision of 2 to 5%) are compared with other experiments and theory. The frequencies are determined mainly by the singlet-triplet energy separations and mixing factors for the He I D-states. The results agree with the same parameters obtained from other recent level-crossing measurements in strong magnetic field mixing of the singlet-triplet states