We propose to supplement the nonlinear ring interferometer (NRI) with two-dimensional feedback, known since 1979, with second feedback loop (FBL) arranged by adding two mirrors. To study the regular and random modes of operation of a dual feedback NRI (DNRI), we have constructed the mathematical model that allows for multiple passes and the model based on loss approximation. The computational algorithms have been constructed and the bifurcation behavior of the DNRI has been analyzed. The data obtained allow determining the sets of DNRI physical parameters that govern the transition from the static mode of operation to the dynamic one (including the deterministic chaos). It is supposed that owing to various turns and time lags of a laser beam in two FBls (when either various systems of coupled oscillators or the system of additional coupling in an oscillator are formed in the DNRI) such an interferometer has advantages as a coder in a system of confidential communication lines.