As part of our program to map the large-scale distribution of galaxies behind the Milky Way, we used the Parkes 210 ft (64m) radio telescope for pointed HI observations of a sample of low surface-brightness (due to heavy obscuration) spiral galaxies selected from the deep optical Zone of Avoidance (ZOA) galaxy catalog in the Hydra/Antlia region (Kraan-Korteweg, 2000, Cat. <J/A+AS/141/123>). Searching a simultaneous velocity range of either 300 to 5500km/s or 300 to 10500km/s to an rms level of typically 2-4mJy resulted in detections in 61 of the 139 pointings, leading to a total of 66 detections (an additional detection was made in a reference position, and two other pointings revealed two and four independent signals respectively). Except for 2 strong HI emitters identified in the shallow Zone of Avoidance HI survey (Henning et al., 2000AJ....119.2686H), all HI detections are new.