The exchange-correlation potentials, fxc(q=0,), to be used in the local-density approximation to the density-functional theory for two-dimensional homogeneous electron liquids in the normal and fully spin-polarized phases are calculated. We make use of accurate Monte Carlo energies and sum rules in the local-field correction, G(q,), to construct fxc(q,) which is valid in the long-wavelength limit. Our results are qualitatively similar to the three-dimensional case. © 1992 The American Physical Society.