This paper presents results of a study of temperature dependences of dielectric response and DC and AC - conductivity in single crystals of the relaxor ferroelectric PbNi1/3Nb2/3O3 (PNN) in a wide range of frequencies (10 Hz - 100 kHz) and temperatures (80 - 750 K). Anomalies in the dielectric response in the form of broad frequency-dependent maxima in the vicinity of 153 and 730 K are observed. The thermal activation character of DC conductivity has been obtained, and activation energies determined as Ea = 770 meV (T > 310 K) and Ea = 23 meV (T <310 K). The analysis of conductivity gives reason to assume the existence of local conductivity in the low-temperature region. It is shown that the conductivity character changes above 350 K from the local to the bulk one. Measurement by thermally stimulated depolarization has shown the presence of a residual polarization below 130 K.