We present in situ pressure experiments on aluminogermanate nanotubes studied by X-ray scattering and absorption spectroscopy measurements. Structural transformations under hydrostatic pressure below 10 GPa are investigated as a function of the morphology, organization, or functionalization of the nanotubes. Radial deformations, ovalization for isolated nanotubes, and hexagonalization when they are bundled are evidenced. Radial collapse of single-walled nanotubes is shown to occur, in contrast to the double-walled nanotubes. The effect of the transmitting pressure medium used on the collapse onset pressure value is demonstrated. Axial Young's moduli are determined for isolated (400 GPa) and bundled (600 GPa) single-walled nanotubes, double-walled nanotubes (440 GPa), and methylated single-walled nanotubes (200 GPa).