A theoretical study is presented of the mechanisms by which freshly nucleated sulfuric acid particles can be grown to the size of cloud condensation nuclei (CCN) in remote marine areas. Three mechanisms are considered: (1) growth by the scavenging and subsequent aqueous phase oxidation of atmospheric SO2, (2) growth by coagulation, and (3) growth by scavenging of atmospheric sulfuric acid. While model calculations indicate that the first two mechanisms are too slow to represent a significant source of CCN in the remote marine atmosphere, scavenging of sulfuric acid can be an effective mechanism for transforming tiny sulfuric acid particles into CCN provided the concentration of preexisting CCN is less than some critical concentration. For conditions typical of the marine boundary layer with ambient SO2 concentrations of about 30 parts per trillion per volume (pptv), we estimate this critical concentration to be quite low (that is, about 1 cm-3). However, under conditions with enhanced SO2 the value of this critical concentration also increases and is estimated to reach a level of about 10 cm-3 when SO2 is equal to 100 pptv. Our calculations suggest that coupling between dimethyl sulfide (DMS) emissions and CCN production in the marine boundary layer can only exist when the existing CCN concentrations at a specific locale fall below this critical concentration. ¿ American Geophysical Union 1992