Third-order nonlinear acoustical tomography is very important for medical diagnostics, because it will provide information on the new and unexplored quantity—third-order nonlinear acoustical parameter. A prototype of the tomography system for reconstructing the distributions of the acoustic nonlinear parameters is developed in our group on the basis of effect of nonlinear noncollinear interaction of three primary waves. Application of coded primary signals with further correlation processing of a detected signal at combination frequencies makes it possible to reconstruct the complete image of an object using three transmitters and one receiver. Third-order effects are born from two competing processes—the pure third order interaction (informational for diagnostic purposes) and the twofold interaction of the second order (interfering). To explore the application boundaries of the third-order nonlinear acoustical tomography, these two competing processes are considered in details. Two cases are compared. In the first case, the interaction takes place between two broadband coded signals and one monochromatic signal. In the second case, all three primary signals are broadband coded; then, amplitude of the interfering part of the signal is smaller. Moreover, in this case, the possibility of reconstructing the spatial distribution of the second and third-order nonlinear acoustical parameters arises due to the reciprocity principle generalized on the nonlinear scattering processes.