Glycolaldehyde, a sugar-related interstellar prebiotic molecule, has recently been detected in two star-forming regions, Sgr B2(N) and G31.41+0.31. The detection of this new species increased the list of complex organic molecules detected in the interstellar medium (ISM) and adds another level to the chemical complexity present in space. Besides, this kind of organic molecule is important because it is directly linked to the origin of life. For many years, astronomers have been struggling to understand the origin of this high chemical complexity in the ISM. The study of deuteration may provide crucial hints. In this context, we have measured the spectra of deuterated isotopologues of glycolaldehyde in the laboratory: the three monodeuterated ones (CH2OD-CHO, CHDOH-CHO and CH2OH-CDO) and one dideuterated derivative (CHDOH-CDO) in the ground vibrational state. Previous laboratory work on the D-isotopologues of glycolaldehyde was restricted to less than 26 GHz. We used a solidstate submillimeter-wave spectrometer in Lille with an accuracy for isolated lines better than 30 kHz to acquire new spectroscopic data between 150 and 630 GHz and employed the ASFIT and SPCAT programs for analysis. We measured around 900 new lines for each isotopologue and determined spectroscopic parameters. This allows an accurate prediction in the ALMA range up to 850 GHz. This treatment meets the needs for a first astrophysical research, for which we provide an appropriate set of predictions.