The formation process of a hydrogen-induced amorphous phase in the C15 Laves phases, RNi2Hx (R=Sm, Gd, Dy, Er) has been examined by X-ray diffraction and differential scanning calorimetry as a function of hydrogenation time. It has been demonstrated that there are two kinds of amorphization processes. That is, the amorphization in SmNi2 and DyNi2 compounds progresses by the nucleation and growth of a hydrogen absorbed amorphous phase. On the contrary, in GdNi2 and ErNi2 a hydrogen absorbed compound transforms polymorphously to the amorphous ones with increasing time. The JMA plot for the process of amorphization gives the numerical exponent n=3.9 for DyNi2 and n=0.5 for GdNi2, respectively. The difference in the process of hydrogen-induced amorphization in these alloys is discussed.