The article discusses the limitations of the Mayr and Cassie linear models and of the Mayr generalized model accompanying the precise mapping of electric arc column within a wide range of changes in bipolar current. The research involved the development of new non-linear hybrid models of arc by the association of linear and non-linear models, the creation of arc hybrid macromodels and the verification (utilising the MATLAB-Simulink software programme) of the efficiency of dynamic voltage-current characteristics through simulations of processes in a simple circuit with electric arc.