The order and other properties of the magnetic phase transitions in the rare-earth ( R)-cobalt Laves phases RCo2 have been studied for R5Gd, Tb, Dy, Ho, Er, Sm, Nd, and Pr by measuring the temperature dependence of the magnetic hyperfine interaction of the nuclear probe 111 Cd on the cubic R sites using the perturbed angular correlation technique. Both for heavy and light R constituents the transitions change from second order ~Gd, Tb, Sm! to first order ~Dy, Ho, Er, Nd, Pr! at order temperatures of 150‐200 K. For heavy R constituents, the order deduced from the hyperfine interaction is in agreement with previous investigations. The observation of first order transitions in NdCo2 and PrCo2, however, is unexpected. In earlier studies the transitions in these compounds are usually classified as second order transitions. Both in the heavy and the light RCo2 the discontinuous jump of the hyperfine interaction at the first order transitions increases with decreasing order temperature. This trend implies that the Co magnetization at the transition increases with decreasing TC which can be related to the temperature dependence of the coefficient of the M 4 term of the free energy in the Wohlfarth-Rhodes-Shimizu theory of itinerant electron magnetism. All compounds investigated presented a spread of the order temperature of ;1 ‐2 K which results in a coexistence of the paramagnetic and the magnetically ordered phase near the transition and causes a critical increase of the relative linewidth of the