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, TbMn2Ge2 and DyMn2Ge2, respectively) and the first-order antiferromagnetic - ferrimagnetic transition at temperature Tt (Tt=96, 80 and 40 K for GdMn2Ge2, TbMn2Ge2 and DyMn2Ge2, respectively) as the temperature decreases. The temperature dependence of the lattice constant a(T) displays a negative magnetoelastic anomaly at the second-order transition point TN and, at the first-order transition Tt, a increases abruptly for GdMn2Ge2 and TbMn2Ge2, Δa/a about 10-3. Nevertheless, the lattice constant c almost does not change at these transition points indicating that such magnetoelastic anomalies are mainly contributed by the Mn-sublattice. The transitions of the magnetoelastic properties are also evidenced on the temperature dependence of magnetic susceptibility χ. The first-order transition behavior at Tt is explained by the Kittel mode of exchange inversion.