For a transponder arrangement having a transponder arranged on an object, in order to achieve longer ranges than would be possible with a purely field-supplied response mode, the transponder is provided with a chargeable electrical energy store. An inductive supply of energy from a pump circuit situated on the object is used to hold the energy store in a charged state. The transponder arrangement can advantageously be interrogated not only in the active mode now made possible, but also in a passive mode which is known per se and is supplied with power purely by the interrogation field.