Experimental results show that Cs adsorbs preferentially on the threefold hollow (H-3) and threefold filled (T-4) sites of the Si(111)7 X 7 reconstructed surface. Following our recent calculations, adsorption of Ge on H-3 or T-4 sites of Si(111)7 x 7 is unfavourable. We present a comparative study of various adsoption mechanisms for Ge and Cs on Si(111)7 X 7, in the framework of the crystalline extension of the extended Huckel theory. We consider the possibility of Cs and Ge adsorption on T-4 and H-3 sites, comer and center adatoms, as well as restatoms. The faulted and unfaulted parts of the 7 X 7 unit cell are distinguished. Adsorption energies and reduced overlap population calculations effectively favour adsorption on the Si dangling bonds for Ge atoms and addition on H-3 and T-4 sites for Cs atoms. The cesium atom has diffuse orbitals, so that, at these positions, it can significantly interact with the dangling bonds despite the long distance. We discuss the differences of the behaviour between germanium and cesium interacting with Si(111)7 X 7.