The theory of the "bridge" effect, i.e., electron tunneling with the participation of intermediate particles, is developed. It is shown and proved that the general incorrectness of the approach that operates with the restricted basis of the bound states on the bridge particles to obtain a subbarrier electron Green's function. This approach is adequate only in the energy region near the bound energy of the bridge centers at the large center-to-center distances. Our theory is based on the concept of multiple subbarrier scattering of tunneling electron on the intermediate particles. The regular method of the calculation of the energies of the collectivized bound states as the poles of the total scattering amplitude is developed. It is shown that the probability of the tunneling transition depends on the value and sign of the amplitude of electron subbarrier scattering on one particle, and this amplitude can be calculated by the variation-asymptotic method developed by the authors earlier. The bridge induced enhancement of the tunneling probability depends exponentially on the length of the bridge, the exponent rises with modulus of the tunneling energy, i.e., with energy decreasing. Such enhancement is possible also in the absence of the bound states on the bridge. Two modes of the tunneling transitions, adiabatic, and nonadiabatic ones, are considered. (C) 2003 American Institute of Physics.