We present the detection of HD absorption lines in the Magellanic Clouds using FUSE space telescope archival data. We found HD in five (including one known) absorption systems in the Large Magellanic Cloud and three systems in the Small Magellanic Cloud. The measured HD column densities, N(HD), vary from 2∙1013 to 2∙1015 cm-2 for associated H2 column densities, NH2, in the range 3∙1019 to 5∙1020 cm-2. Using Hubble Space Telescope archival data, we also determined the population of CI fine-structure levels and metallicities in these systems. The modelling of obtained observational data for HD, H2 and C I allow us to estimate physical conditions in the interstellar medium of the Magellanic Clouds associated with these absorption systems, namely, the cosmic ray ionization rate, ultraviolet field intensity and number density.