A thin metallic cobalt (Co) layer was deposited on a single-crystal Ge (001) surface at room temperature by the electron-beam evaporation of a pure Co metal source in an ultrahigh-vacuum transmission electron microscope. The formation and epitaxial growth of a cobalt germanide Co5Ge7 phase on the Ge (001) surface was studied in situ by gradually heating the sample from room temperature to ∼350 °C. The occurrence of an epitaxial hexagonal-close-packed Co and the reaction between Co and Ge were observed at ∼225 °C. After annealing at ∼300 °C for 26.5 h, a continuous epitaxial Co5Ge7 film formed on the Ge (001) substrate. With further annealing at a higher temperature, the continuous Co5Ge7 layer broke up and formed three-dimensional islands in order to relieve the strain energy in the epitaxial Co5Ge7 layer. Two epitaxial relationships between Co5Ge7 and Ge, i.e., Co5Ge7<110>(001)//Ge<100>(001) and Co5Ge7<001>(110)//Ge<100>(001) were found by electron diffraction.