Recent experimental results for the magnetic hyperfine field B hf at the nuclei of s-p impurities such as 119 Sn in intermetallic Laves phases RM 2 (R = Gd, Tb, Dy, Ho, Er; M = Fe, Co) and 111 Cd in RCo 2 , the impurity occupying a R site indicate that the ratio B hf /µ 3d exhibits different behavior when one goes from RFe 2 to RCo 2 . In this work, we calculate these local moments and the magnetic hyperfine fields. In our model, B hf has two contributions: one arising from the R ions, and the other arising from magnetic 3d-elements; these separate contributions allow the identification of the origin of different behavior of the ratio mentioned above. For 111 Cd in RCo 2 we present also the contributions for B hf in the light rare earth Pr, Nd, Pm, Sm compounds. For the sake of comparison we apply also the model to 111 Cd diluted in RNi 2 . Our self-consistent magnetic hyperfine field results are in good agreement with those recent experimental data.