We present the results of neutral hydrogen (HI) observations of the NGC 5044 and NGC 1052 groups, as part of a GEMS (Group Evolution Multiwavelength Study) investigation into the formation and evolution of galaxies in nearby groups. Two new group members have been discovered during a wide-field HI imaging survey conducted using the ATNF Parkes telescope. These results, as well as those from follow-up HI synthesis and optical imaging, are presented here. J1320 - 1427, a new member of the NGC 5044 group, has an HI mass of and , with a radial velocity of v= 2750 kms-1. The optical galaxy is characterized by two regions of star formation, surrounded by an extended, diffuse halo. J0249-0806, the new member of the NGC 1052 group, has and v= 1450 kms-1. The optical image reveals a low-surface-brightness galaxy. We interpret both of these galaxies as irregular type, with J0249 - 0806 possibly undergoing first infall into the NGC 1052 group.