Conductivity mechanism in the regime of the intrinsic Josephson effect in layered superconductors with singlet d-wave pairing is studied theoretically. The cases of coherent and incoherent interlayer tunneling of electrons are considered. The theory with coherent tunneling describes main qualitative features of the effect observed in highly anisotropic high-T$_c$ superconductors at voltages smaller than the amplitude of the superconducting gap, mechanism of the resistivity being related to excitations of the quasiparticles via the d-wave gap. At voltages of the order of the gap amplitude and larger, the I-V curves are better described by the incoherent tunneling. Interaction of the Josephson junctions formed by the superconducting layers due to charging effects is shown to be small.