UFe2 (Laves phase, fee crystal structure) is a ferromagnet with T-C=165 K, Previous neutron elastic measurements have established that the Fe moment is 0.6 mu(B) and that the moment on the U atom is almost zero because of the cancellation of the spin and orbital moments, which are both about 0.23 mu(B), but are oppositely directed. We have now examined the spin dynamics from a large single crystal with both thermal and cold-source triple-axis spectrometers. Comparisons with the extensive work performed on RFe(2)(R=Tb, Ho, Er) suggests that two dispersive modes should be seen at low energy (i.e., less than similar to 20 meV). However, only one mode has been found in UFe2 and this involves the precession of the Fe spins. We propose that the acoustic mode involving the uranium spin is sufficiently broadened in (q,omega) space that we cannot readily detect the excitation. Nevertheless, the influence of the U-Fe exchange may be seen in (a) the presence of a gap in the Fe spin-wave spectrum at q=0, and (b) in an increase in the Fe spin-wave stiffness constant (D) as compared to that found in pure Fe. This last property is a direct consequence of the hybridization between the U5f and Fe3d electrons. We find also that D is strongly temperature dependent, presumably due to two-magnon interactions. Thus, this effect, together with the low moment on the Fe atoms, results in the comparatively low, as compared to the RFe(2) compounds, T-C of 165 K in UFe2.