Morphological evolution of cobalt germanide epilayers, CoxGey, was investigated in situ by scanning tunneling microscopy and spectroscopy and reflection high-energy electron diffraction, as a function of deposition method and, hence, the phase content of the epilayer. During reactive deposition epitaxy, in which Co atoms were evaporated onto a flat pseudomorphic Ge/Si(001) wetting layer at 773 K, the first phase formed was cobalt digermanide, CoGe2, in the form of elongated pyramidal islands. Each of these three-dimensional islands has locally exerted an additional strain on the Ge wetting layer already strained at the Ge/Si(001) interface, lifting the layer metastability and causing, in turn, the formation of three-dimensional Ge pyramids underneath every CoGe2 island. Solid-phase epitaxy of Co onto the same Ge/Si(001) epilayer resulted in the formation of more Co-rich germanide islands. Coupling of strain from these germanides to the epitaxial Ge/Si(001) strain has also facilitated a two-dimensional-to-three-dimensional transition of the Ge layer, however, with the germanide islands located at the Ge pyramid troughs, rather than crests. The difference in the relative location of germanide and germanium islands in these two cases is explained by accommodation of the large lattice-constant germanides at the more relaxed regions of the Ge pyramid crests and the smaller lattice-constant at the compressed Ge pyramid troughs.