The magnetic behavior of the Fe sublattice in the pseudobinary Laves phase materials (Hf,Mo)Fe2 was thoroughly investigated in the paramagnetic regime as well as in the magnetically ordered state. The analysis of the paramagnetic phase has led to the determination of the Curie-Weiss temperature and effective paramagnetic moment whereas the spontaneous magnetic moment was obtained at temperatures ranging from 4 K up to the Curie point. The number of magnetic charge carriers was calculated both above and below the ferromagnetic ordering temperature in order to evaluate the degree of itinerancy (degree of delocalization) of Fe magnetism in the Hf1-xMoxFe2 series of intermetallic compounds. It is shown that the Curie and Curie-Weiss temperatures decrease strongly upon increasing Mo concentration. Of particular interest is the thermal dependence of the reciprocal magnetic susceptibility in the intermediate composition range (0.05 x 0.15): an unusual transition between two distinct Curie-Weiss behaviors is observed at a critical temperature T & lowast;. The experimental data were analyzed and discussed within the framework of the Kuz'min's model, the self-consistent renormalization and Takahashi's theory of spin fluctuations. T0 and TA parameters characterizing the widths of the spin fluctuation spectrum in energy and wave-vector space, respectively, have been estimated. The transverse spin fluctuations are predominant for the parent intermetallic HfFe2, in contrast, the longitudinal spin fluctuations gradually grow for the richest Mo compositions. Furthermore, Mo for Hf substitution induces a weakening of ferromagnetic exchange interactions: a change from long-range ferromagnetism (for HfFe2) towards systems with competing exchange interactions (for Mo-rich side) is observed. In this family of compounds, the generalized RhodesWohlfarth ratio points out an itinerant magnetism. The 3d Fe magnetism evolves from nearly localized character to strongly delocalized one as the Mo fraction is increased.