The redshift dependence of the fraction of galaxies which are merging or strongly interacting is a steep function of Ω and depends on the ratio of the cutoff velocity for interactions to the pairwise velocity dispersion. For typical galaxies the merger rate is shown to vary as (1 + z)m, where m ≃ 4.51Ω0.42, for Ω near 1 and a CDM-like cosmology. The index m has a relatively weak dependence on the maximum merger velocity, the mass of the galaxy, and the background cosmology, for small variations around a cosmology with a low redshift, z ≈ 2, of galaxy formation. Estimates of m from optical and IRAS galaxies have found that m ≃ 3-4, but with very large uncertainties. If quasar evolution follows the evolution of galaxy merging and m for quasars is greater than 4, then Ω > 0.8. More data at relatively low redshifts, z ≈ 0.5, will greatly strengthen this estimate. © 1990. The American Astronomical Society. All tights reserved.