We use Interferometric Synthetic Aperture Radar (InSAR) to search for surface deformation in the southern Andes (40¿S--46¿S and 49¿S--53¿S) associated with magmatic processes. Although the available data are not optimal, we can constrain the amount of volcanic deformation at about 27 Holocene volcanoes between the years 1993--1999. We detect inflation of Cerro Hudson volcano following its 1991 eruption, and use spherical and non-spherical models to constrain the source of deformation to be between 4 and 8 km below sea level. We measure the rate of deformation to be about 5 cm/year in the radar line-of-sight, and infer that the maximum deformation could exceed 10 cm/year in the center of the caldera. Within the errors of the measurements, the rate of deformation is constant from 1993--1998 (10--30 ¿ 106 m3/year). At this rate, 100--200 years is required to accumulate the volume of material erupted in 1991.