[en] Nb₃Sn is a promising material for superconducting (s.c.) accelerators because of its high critical temperature of 18.2 K and high thermodynamic critical field of 535 mT. Compared to Nb significantly reduced rf losses and higher accelerating fields should be possible at operation temperatures of about 4.2 K especially for frequencies between 1 and 6 GHz. The presently used Nb accelerating structures can be coated with a Nb₃Sn layer by the vapor diffusion technique. We have formed uniform Nb₃Sn layers on 1 and 3 GHz single and multicell accelerating structures in specially constructed UHV furnaces. At 4.2 K and low rf fields quality factors of 10¹⁰ (1 GHz) and 7 · 10⁹ (3 GHz) have been achieved which are reduced by a factor of about three at the maximum accelerating fields between 4 and 7.2 MV/m. This paper discusses the BCS surface resistance as well as anomalous loss mechanisms and field limitations investigated by multimode measurements and temperature mapping. First results obtained in a Nb₃Sn coated 3 GHz single-cell cavity made of high purity niobium are promising