Abstract We report 73 Ge-NMR/NQR measurements on the itinerant ferromagnetic (FM) superconductor UGe 2 at P =1.2 GPa. The temperature ( T ) dependence of the nuclear spin lattice relaxation rate (1/ T 1 ) at zero field has demonstrated the onset of the superconducting (SC) transition at T c =0.7 K. The lack of a coherence peak in 1/ T 1 just below T c , followed by a T 3 -like behavior, provide compelling evidence for the unconventional nature of the SC state that coexists with the FM state on a microscopic scale in UGe 2 .