In the present work, we investigated the mechanical alloying of binary Ga-Se(1:1) and Ga-Te(1;1) sysyems. The high-energy ball-milling was performed at $40^{circ}C$ where one of constituents (Ga) is molten state. The purpose of the work was to see whether reactions between constituent elements are accelerated by the presence of a liquid phase. During the ball-milling, the liquid Ga phase completely disappeared and the resulting powders consist of nanocrystalline grain of ~20 nm with partly amorphized phases. However, no intermetallic compounds formed in spite of the presence of the liquid phases which has much higher diffusivity than solid constituents. By subsequent heat-treatments, the intermetallic compounds such as GaSe and GaTe formed at relatively low temperatures. The formation temperature of theses compound was much lower than those predicted by equilibrium phase diagram. The comparison of the ball-milled powders with un-milled ones indicated that the easy formation of intermetallic compound or allying occurs at low temperatures.