G-frames,　which　were　considered　recently　as　generalized　frames　in　Hilbert　spaces,　have　many　properties　similar　to　those　of　frames,　but　not　all　the　properties　are　similar.　For　example,　exact　frames　are　equivalent　to　Riesz　bases,　but　exact　g-frames　are　not　equivalent　to　g-Riesz　bases.　In　this　paper,　we　firstly　give　a　characterization　of　an　exact　g-frame　in　a　complex　Hilbert　space.　We　also　obtain　an　equivalent　relation　between　an　exact　g-frame　and　a　g-Riesz　basis　under　some　conditions.　Lastly　we　consider　the　stability　of　an　exact　g-frame　for　a　Hilbert　space　under　perturbation.　These　properties　of　exact　g-frames　for　Hilbert　spaces　are　not　similar　to　those　of　exact　frames.　(C)　2010　Elsevier　Inc.　All　rights　reserved.