  We report $^{31}$P NMR measurements under various magnetic fields up to 7 T
for the intermediate valence compound EuNi$_2$P$_2$, which shows heavy
electronic states at low temperatures. In the high-temperature region above 40
K, the Knight shift followed the Curie--Weiss law reflecting localized $4f$
states. In addition, the behavior corresponding to the temperature variation of
the average valence of Eu was observed in the nuclear spin-lattice relaxation
rate $1/T_1$. With the occurrence of the Kondo effect, $1/T_1$ was clearly
reduced below 40 K, and the Knight shift becomes almost constant at low
temperatures. From these results, the formation of heavy quasiparticles by the
hybridization of Eu $4f$ electrons and conduction electrons was clarified from
microscopic viewpoints. Furthermore, a characteristic spin fluctuation was
observed at low temperatures, which would be associated with valence
fluctuations caused by the intermediate valence state of EuNi$_2$P$_2$.
