BaCoX2O7 ( X = As, P) are built on magnetic 1D units in which strong aperiodic undulations originate from incommensurate structural modulations with large atomic displacive amplitudes perpendicular to the chain directions, resulting in very unique multiferroic properties. High-pressure structural and vibrational properties of both compounds have been investigated by synchrotron X-ray powder diffraction and Raman spectroscopy at room temperature and combined with density functional calculations. A structural phase transition is observed at 1.8 GPa and 6.8 GPa in BaCoAs 2 O 7 and BaCoP2O 7 , respectively. Sharp jumps are observed in their unit-cell volumes and in Raman mode frequencies, thus confirming the first-order nature of their phase transition. These transitions involve the disappearance of the modulation from the ambient-pressure polymorph with clear spectroscopic fingerprints, such as reduction of the number of Raman modes and change of shape on some peaks. The relation between the evolution of the Raman modes along with the structure are presented and supported by density functional theory structural relaxations.