The spontaneous magnetic transitions and corresponding magnetoelastic properties of intermetallic compounds RMn2Ge2(R=Gd, Tb and Dy) were investigated by using the X-ray diffraction method and magnetic measurement. The results showed that the compounds experience two magnetic transitions, namely the second-order paramagnetic to antiferromagnetic transition at temperature TN(TN=368, 423 and 443 K for GdMn2Ge2, TbMn2Ge2and DyMn2Ge2, respectively) and the first-order antiferromagnetic - ferrimagnetic transition at temperature Tt(Tt=96, 80 and 40 K for GdMn2Ge2, TbMn2Ge2and DyMn2Ge2, respectively)...