The solid state reaction by mechanical alloying(MA) generally proceeds by lowering the free energy as the result of a chemical reaction at the interface between the two adjacent layers. However, Lee et $al.^{1-5)}$ reported that a mixture of Cu and Ta, the combination of which is characterized by a positive heat of mixing of +2kJ/mol, could be amorphized by mechanical alloying. This implies that there exists an up-hill process to raise the free energy of a mixture of pure Cu and la to that of an amorphous phase. It is our aim to investigate to what extent the MA is capable of producing a non-equilibrium phase with increasing the heat of mixing. The system chosen was the ternary $Cu_{30}Ta_{ 70-x}Mo_ x$ (x=35, 10). The mechanical alloying was carried out using a Fritsch P-5 planetary mill under Ar gas atmosphere. The MA powders were characterized by the X-ray diffraction with Cu-K $alpha$ radiation, thermal analysis, electron diffraction and TEM micrographs. In the case of x=35, where pure Cu powders were mixed with equal amount of pure Ta and Mo powders, we revealed the formation of bcc solid solution after 150 h milling but its gradual decomposition by releasing fcc-Cu when milling time exceeded 200 h. However, an amorphous phase was clearly formed when the Mo content was lowered to x=10. It is believed that the amorphization of ternary $Cu_{30}Ta_{60}Mo_{10}$ powders is essentially identical to the solid state amorphization process in binary $Cu_{30}Ta_{70}$ powders.