The thermal expansion and anisotropic magnetostriction of the RCo 2 Laves phases were studied in the temperature range 4-500 K using the X-ray powder diffraction method. In the heavy RCo2 the magnetic moment of the itinerant d electron subsystem derived from the magnetovolume effect was found to fit well with the magnetization curve of YCo2. A pronounced paraprocess above the metamagnetic transition has been observed when increasing the f-d exchange field. The type and temperature variation of the distortion of the cubic unit cell of the three compounds PrCo2, NdCo2 and SmCo2 have been studied in detail. The corresponding magnetostriction constants lambda 111 or lambda 100 were calculated. At 4 K the following values have been obtained: PrCo2, tetragonal distortion, easy axes (100), lambda 100=-3.4*10-3: SmCo2, rhombohedral distortion, easy axes (111), lambda 111=-4.6*10-3; NdCo2, tetragonal distortion and easy axes (100) for 42 K<T<Tc, orthorhombic distortion and easy axes (110) for T<42 K with mod lambda 111 mod =1.9*10-3 and lambda 100=-4.6*10-3.