The magnetization curves along the main crystallographic directions of single crystalline ErGa2 and Dy3Co samples have been measured in both steady and pulse magnetic fields. Both compounds are antiferromagnets with a strong magnetocrystalline anisotropy and exhibit metamagnetic transitions to the field-induced ferromagnetic state. In steady field, a two-steps-like metamagnetic transition through an intermediate ferri-magnetic phase was observed along the c axis of ErGa2 and along the [100] (a) axis of Dy3Co. Alternatively, in pulse fields the metamagnetic transition in both compounds occurs as a single step and is accompanied by heating of the samples. Owing to the quasiadiabatic pulse field magnetization process the temperature growth may exceed 20 K. The shape of the magnetization curves in pulse fields was found to depend strongly on the field sweep rate and on the initial temperature of the sample. The obtained results have been discussed in terms of the thermally activated nucleation of ferri- and ferromagnetic phases, the appearance and the relaxation of the metastable exited states of R-ions.