We report the discovery of a large population of dwarf irregular galaxies in the two nearest groups of galaxies outside the Local Group, the Sculptor and the Centaurus A groups (2.5 and 3.5 Mpc). Total areas of approximately 940 and 910 square degrees in these groups were scanned visually on the SRC J films to find dwarf candidates. Redshifts were obtained by an HI survey carried out at Parkes, with detection limits of 4 imes 10^6 Msun and 7.8 imes 10^6 Msun , and 33 dwarf galaxies were successfully detected in the groups. A follow-up optical survey (Halpha spectroscopy) detected a few more, and confirmed most of the HI redshifts. A total of 16 and 20 dwarf galaxies are found in Sculptor and Centaurus A, of which 6 are newly identified objects, and 5 more have newly determined redshifts. In both groups the dwarf members show a wider spatial and velocity distribution than the brighter members. From their radial velocities and projected distances we estimate the crossing times of the groups, which confirm that they are not yet virialised.Comment: 35 pages Latex (aaspp4.sty) including all tables and 7 postscript figures. Figs 1,2,3 available at ftp://ftp.hq.eso.org/incoming/scote Submitted to A