A series of (GdxDy1-x)Co2 (0-0.55) compounds have been prepared by arc-melting method. In order to determine the phase transition order in these compounds, we have performed some magnetization measurements. Only from the plots of temperature dependence of magnetization and the low-field magnetization isotherms, it is difficult to judge the phase transition order. The low-field Arrott plot is proved to be a more reliable method to characterize the first-order transition and the second-order transition. No first-order transition is observed in (GdxDy1 x)Co2 compounds (xa0). The result is discussed in the Inoue-Shimizu like model.