We consider a compositionally and entropically stratified, compressible, rotating fluid earth and study gravitational-viscoelastic perturbations of its hydrostatic initial state. Using the Lagrangian representation and assuming infinitesimal perturbations, we deduce the incremental field equations and interface conditions of {\em gravitational viscoelastodynamics} (GVED) governing the perturbations. In particular, we distinguish the {\em material}, {\em material-local} and {\em local} forms of the incremental equations. We also demonstrate that their short-time asymptotes correspond to generalizations of the incremental field equations and interface conditions of {\em gravitational elastodynamics} (GED), whereas the long-time asymptotes agree with the incremental field equations and interface conditions of {\em gravitational viscodynamics} (GVD). The incremental thermodynamic pressure appearing in the long-time asymptote to the incremental constitutive equation is shown to satisfy the appropriate incremental state equation. Finally, we derive approximate field theories applying to gravitational-viscoelastic perturbations of isocompositional, isentropic and compressible or incompressible fluid domains.