Glyoxal and methylglyoxal are scavenged by clouds, where a fraction of these compounds are oxidized during the lifetime of the droplet. As a cloud droplet evaporates, the remaining glyoxal and methylglyoxal must either form low-volatility compounds such as oligomers and remain in the aerosol phase, or transfer back to the gas phase. A series of experiments on evaporating aqueous aerosol droplets indicates that over the atmospherically relevant concentration range for clouds and fog (4-1000 microM), 33 +/- 11% of glyoxal and 19 +/- 13% of methylglyoxal remains in the aerosol phase while the remainder evaporates. Measurements of aerosol density and time-dependent AMS signal changes are consistent with the formation of oligomers by each compound during the drying process. Unlike glyoxal, which forms acetal oligomers, exact mass AMS data indicates that the majority of methylglyoxal oligomers are formed by aldol condensation reactions, likely catalyzed by pyruvic acid, formed from methylglyoxal disproportionation. Our measurements of evaporation fractions can be used to estimate the global aerosol formation potential of glyoxal and methylglyoxal via self-reactions at 1 and 1.6 Tg C yr(-1), respectively. This is a factor of 4 less than the SOA formed by these compounds if their uptake is assumed to be irreversible. However, these estimates are likely lower limits for their total aerosol formation potential because oxidants and amines will also react with glyoxal and methylglyoxal to form additional low-volatility products.