  The quantum electrodynamic theory of the nuclear recoil effect on the atomic
g factor to all orders in \alpha Z and to first order in m/M is formulated. The
complete \alpha Z-dependence formula for the recoil correction to the
bound-electron g factor in a hydrogenlike atom is derived. This formula is used
to calculate the recoil correction to the bound-electron g factor in the order
(\alpha Z)^2 m/M for an arbitrary state of a hydrogenlike atom.
