In order to clarify the mechanism of the fast localized motion of hydrogen in the cubic (C15-type) Laves phase YMn2, we have performed quasielastic neutron scattering measurements in YMn2Hx (x = 0.6 and 1.2) over the temperature range 10 - 376 K. The behaviour of the elastic incoherent structure factor as a function of momentum transfer ( studied up to Q(max) approximate to 3 angstrom(-1)) is consistent with the two-site motion of H atoms within pairs of closely spaced interstitial g (Y2Mn2) sites. Comparison of the data for YMn2H0.6 and YMn2H1.2 shows that both the hydrogen jump rate and the fraction of H atoms participating in the fast localized motion decrease with increasing H content.