High-resolution spectra of 35 F main-sequence stars have been obtained at high SNRs in the region of the Li I resonance line at 6708 A. Fourteen of the stars are members of the Hyades, six are members of Praesepe, and the remaining 15 stars are members of the Hyades Moving Group. Equivalent widths of the Li resonance line and of Fe lines in the same spectral region were measured and Li and Fe abundances were calculated from spectral synthesis using Kurucz model atmospheres. A mean metallicity of (Fe/H) = + 0.17 + or - 0.06 for the Hyades, + 0.13 + or - 0.07 for Praesepe, and + 0.11 + or - 0.09 for the Hyades Moving Group is obtained. The Li abundance patterns are consistent with those found previously for the Hyades stars and for the Praesepe stars, but some of the Hyades Moving Group members do not fit this Li-temperature profile well. The possibility exists that the Hyades Moving Group is not coeval and that its members have little in common other than kinematics.