High precision measurements were taken of the specific volume of glassy germanium chalcogenides GeSe2, GeS2, Ge17Se83, and Ge8Se92 under hydrostatic pressure to 8.5 GPa. For GeSe2 and GeS2 glasses in the pressure range to 3 GPa the behavior is an elastic one with bulk modulus softening at pressures above 2 GPa. At higher pressures the relaxation processes begin that have logarithmic kinetics. The relaxation rate for GeSe2 glasses has a clearly pronounced maximum at 3.5-4.5 GPa, which is indicative of the existence of several mechanisms of structural transformations. For nonstoichiometric glasses inelastic behavior is observed at pressures above 1-1.5 GPa, the relaxation rate being much less than that for stoichiometric ones. For all the glasses we observe the loss of memory about the prehistory: A pressure rising after relaxation causes the return of values of the specific volume to the curve of compression without relaxation. After depressurization the residual densification makes up nearly 7% in stoichiometric glasses and 1.5% in Ge17Se83 glasses. The values of the effective bulk modulus for nonstoichiometric glasses coincide upon pressure lowering with the values after isobaric relaxations during pressure increase, whereas for GeSe2 the moduli during the decompression exceed substantially the values after isobaric relaxations at compression path. The results obtained demonstrate high capacity of the volumetric measurements to reveal the nature of the transformations in glassy germanium chalcogenides under compression.