Aim. The synthesis, computer modeling and field experimental research of two degree of freedom robust two circuit system of active shielding of magnetic field with circular space-time characteristic, generated by overhead power lines with «triangle» type of phase conductors arrangements and with different shielding coils spatial positions for reducing the magnetic flux density to the sanitary standards level and to reducing the sensitivity of the system to plant parameters uncertainty. Methodology. The synthesis is based on the multi-criteria game decision, in which the payoff vector is calculated on the basis of the Maxwell equations quasi-stationary approximation solutions. The game decision is based on the stochastic particles multiswarm optimization algorithms. The initial parameters for the synthesis by system of active shielding are the location of the overhead power lines with respect to the shielding space, geometry and number of shielding coils, operating currents, as well as the size of the shielding space and magnetic flux density normative value, which should be achieved as a result of shielding. The objective of the synthesis is to determine their number, configuration, spatial arrangement and shielding coils currents, the control systems parameters as well as the resulting of the magnetic flux density value at the shielding space. Results. Computer simulation and field experimental research results of two degree of freedom robust two circuit system of active shielding of magnetic field, generated by overhead power lines with «triangle» type of phase conductors arrangements and with different shielding coils spatial positions are given. The possibility of initial magnetic flux density level reducing and system sensitivity to the plant parameters uncertainty reducing is shown. Originality. For the first time the synthesis, theoretical and experimental research of two degree of freedom robust two-circuit t system of active shielding of magnetic field generated by single-circuit overhead power line with phase conductor's triangular arrangements and with different shielding coils spatial positions carried out. Practical value. Practical recommendations from the point of view of the practical implementation on reasonable choice of the spatial arrangement of two shielding coils of robust two-circuit system of active shielding of the magnetic field with circular space-time characteristic generated by single-circuit overhead power line with phase conductor's triangular arrangements are given. References 32, figures 20.