  We have performed ^{31}P-NMR measurements on Ce(Ru_{1-x}Fe_{x})PO in order to
investigate ferromagnetic (FM) quantum criticality, since heavy-fermion (HF)
ferromagnet CeRuPO with a two-dimensional structure turns to a HF paramagnet by
an isovalent Fe-substitution for Ru. We found that Ce(Ru_{0.15}Fe_{0.85})PO
shows critical fluctuations down to \sim 0.3 K, as well as the continuous
suppression of Curie temperature and the ordered moments by the
Fe-substitution. These experimental results suggest the presence of a FM
quantum critical point (QCP) at x \sim 0.86, which is a rare example among
itinerant ferromagnets. In addition, we point out that the critical behaviors
in Ce(Ru_{0.15}Fe_{0.85})PO share the similarity with those in YbRh_{2}Si_{2},
where the local criticality of $f$ electrons has been discussed. We reveal that
Ce(Ru_{1-x}Fe_{x})PO is a new system to study FM quantum criticality in HF
compounds.
