A transponder apparatus for a transponder unit has a UHF and HF transponder The UHF transponder has a transponder support, a UHF antenna and a UHF chip. The HF transponder has an HF antenna and an HF chip. The UHF antenna is at the transponder support and is made up of conducting UHF antenna structures in transponder support planes which are spatially separated from one another. The transponder apparatus includes an electrically-insulating attachment layer connecting the UHF transponder to the HF antenna. The transponder apparatus includes an electrically-insulating spacer element connected to the HF transponder and which spatially separates the UHF transponder and the HF transponder relative to a body. The UHF transponder is disposed on the HF antenna. A conducting HF antenna structure of the HF antenna extends beyond a covering surface of the UHF transponder and the HF antenna structure.