The flowing of induced currents in electric machines, especially in the dampers or massive parts of large synchronous machines, implies an increase in the order of the equivalent circuits used to model their frequency response. But physical meanings of the circuit parameters are often lost. Thus, the authors propose to go back over the modeling of induced currents, in order to define noninteger order equivalent circuits which would be closely linked with the consequences of induced currents on the frequency response. In this paper, the proposed equivalent circuit is based on half-order systems. It is used to represent the frequency response of 1101-NIVA turbo-alternator and 6-MVA hydro-alternator. The identification results are compared with measurements.