The ac responses of the ZnO pellets have been studied by ac measurements (impedance, capacitance and phase angle) over the temperature range 300 - 435 K. The ac conductivity of the ZnO pellets is observed to be proportional to omega(s), where omega is the angular frequency and the exponent s is a temperature- and frequency-dependent parameter. Based on the existing theories of ac conduction, it has been concluded that for low frequency region (20 Hz - 2 kHz), the dominant conduction mechanism in the ZnO pellets is multihopping at all temperatures, whereas for high frequency region (500 kHz - 2 MHz), the small polaron tunneling model is the dominant mechanism in the pellets. Activation energies for ac conduction processes are estimated to be in the range of 0.028 - 0.277 eV which are found to vary with the frequency of the ac signal. These results are found to be consistent with the hopping model. The ac capacitance and the dielectric loss tangent are found to be dependent on both frequency and temperature. Such dependences have been explained taking into account the equivalent circuit model comprising a frequency-independent capacitive element in parallel with a temperature-dependent resistive element, both in series with a low value resistance. Impedance spectroscopy studies show single semicircular arcs in the complex impedance spectra at all temperatures in the range 300 - 435 K, with their centres lying below the real axis at a particular angle of depression indicating a multirelaxation behaviour in the pellets.