Sent to Geophysical Journal International on July 29, 2003.This paper deals with the spectral element modeling of seismic wave propagation at the global scale.Two aspects relevant to low-frequency studies are particularly emphasized.First, the method is generalized beyond the Cowling approximation in order to fully account forthe effects of self-gravitation.In particular, the perturbation of the gravity field outside the Earth is handled by a projection of thespectral element solution onto the basis of spherical harmonics.Second, we propose a new formulation inside the fluid which allows to account for anarbitrary density stratification.It is based upon a decomposition of the displacement into two scalar potentials, and results ina fully explicit fluid-solid coupling strategy.The implementation of the method is carefully detailed and its accuracy is demonstrated through a seriesof benchmark tests