Heterogeneous sulfate production in the remote marine boundary layer is studied by combining measurements collected during the first Southern Hemisphere marine Aerosol Characterization Experiment (ACE 1) with two numerical models: one simulating heterogeneous sulfate production in sea-salt aerosol water (SSAW) and the other simulating cloud processing. The models calculate oxidation of SO2 by O3 and H2O2 via aqueous-phase reactions both in SSAW and in cloud droplets. Model calculations indicate that as much as 50--75% of the observed non-sea-salt (NSS) sulfate in particles in the ambient diameter size range of 0.9--16 μm during the ACE 1 measurement period is due to production in SSAW with cloud processing producing the remainder. The initial alkalinity of the wind-generated sea-salt aerosols can strongly influence sulfate production. Changing the effective alkalinity of SSAW from a value typical of seawater to a value based on the measurements taken at Cape Grim results in a better match to the observed NSS sulfate size distribution with up to 75% of the predicted supermicrometer NSS sulfate being due to heterogeneous conversion in SSAW. The average rates of removal of sulfate due to dry and wet deposition for the 0.4--16 μm size range are 38 and 14 ng m-3d-1 respectively.