In this study a steady-state equivalent circuit for a brushless doubly fed machine (BDFM), based upon earlier work, is introduced which takes account of core losses. Based upon some loss approximations, simple relationships have been derived, which show that the synchronous mode operation, in terms of core loss, of the BDFM is similar to the cascaded doubly fed machine. The slip-dependence of core loss resistances in the equivalent circuit has been investigated by applying energy conservation to derive machine steady-state torque-speed relations in the presence of core loss. Experimental speed measurements of the BDFM in the simple induction mode were used to identify the core loss resistance values.