The dynamics of intense Langmuir waves in current-carrying plasmas is studied both analytically and numerically. Starting with the widely used Zakharov equations, adapted to these systems, specific features of this problem are pointed out. Further, the role of resonant particles is analyzed. By using 1-D macroparticle numerical code, nonlinear regimes of the modified-decay and modulational instabilities are then modelled. Efficient cooperation of essentially ponderomotive and electron-ion drift effects its demonstrated. It appears that the heating of a current-carrying plasma can be activated through releasing of the inductively stored energy, due to the enhanced conversion of energy associated with the electron drift motion. The underlying physics is discussed and its relationship to solar flare theory is suggested.