  We suggest a theory of internal coherent tunneling in the pseudogap region,
when the applied voltage U is below the free electron gap 2Delta_0. We address
quasi 1D systems, where the gap is originated by spontaneous lattice
distortions of the Incommensurate Charge Density Wave (ICDW) type. Results can
be adjusted also to quasi-1D superconductors. The instanton approach allows to
calculate the interchain tunneling current both in single electron (amplitude
solitons, i.e. spinons) and bi-electron (phase slips) channels. Transition
rates are governed by a dissipative dynamics originated by emission of gapless
phase excitations in the course of the instanton process. We find that the
single-electron tunneling is allowed below the nominal gap 2Delta_0 down to the
true pair-breaking threshold at 2W_as<2Delta, where W_as=2Delta/pi is the
amplitude soliton energy. Most importantly, the bi-electronic tunneling
stretches down to U=0 (in the 1D regime). In both cases, the threshold behavior
is given by power laws J (U-U_c)^beta, where the exponent beta v_F/u is large
as the ratio of the Fermi velocity v_F and the phase one u. In the 2D or 3D
ordered phases, at temperature T<T_c, the one-electron tunneling current does
not vanish at the threshold U_c anymore, but saturates above it at U-U_c
T_c<<Delta. Also the bi-particle channel acquires a finite threshold U_c=W_ph
T_c<<Delta at the energy W_ph of the 2\pi phase soliton.
