GaGeTe is a layered topological semimetal that has been recently found to exist in at least two different polytypes, a-GaGeTe (R3m) and b-GaGeTe (P63mc). Here we report a joint experimental and theoretical study of the structural, vibrational, and electronic properties of these two polytypes in high-pressure conditions. Both polytypes show anisotropic compressibility and two phase transitions, above 7 and 15 GPa, respectively, as confirmed by XRD and Raman spectroscopy measurements. Although the nature of the high-pressure phases could not be confirmed, comparison with other chalcogenides and total -energy calculations allow us to propose possible high-pressure phases for both polytypes with an in-crease in coordination for Ga and Ge atoms from 4 to 6. In particular, the simplification of the X-ray pattern for both polytypes above 15 GPa suggests a transition to a structure of relatively higher symmetry than the original one. This result is consistent with the rocksalt-like high-pressure phases observed in parent III-VI semiconductors, such as GaTe, GaSe, and InSe. Pressure-induced amorphization is observed upon pressure release. The electronic band structures of a-GaGeTe and b-GaGeTe and their pressure dependence also show similarities to III-VI semiconductors, thus suggesting that the germanene-like sublayer induces a semimetallic character in both GaGeTe polytypes. Above 3 GPa, both polytypes lose their topological features, due to the opening of the direct band gap, while the reduction of the interlayer space increases the thermal conductivity at high pressure. & COPY; 2023 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).