Nonlinear　Galerkin　Methods　(NGMs)　are　numerical　schemes　for　evolutionary　partial　differential　equations　based　on　the　theory　of　Inertial　Manifolds　(IMs)[1]　and　Approximate　Inertial　Manifolds　(AIMs)[2].　In　this　paper,　we　focus　our　attention　on　the　2-D　Navier-　Stokes　equations　with　periodic　boundary　conditions,　and　use　Fourier　methods　to　study　its　nonlinear　Galerkin　approximation　which　we　call　Fourier　Nonlinear　Galerkin　Methods　(FNGMs)　here.　The　first　part　is　contributed　to　the　semidiscrete　case.　In　this　part,　we　derive　the　well-posedness　of　the　nonlinear　Galerkin　form　and　the　distance　between　the　nonlinear　Galerkin　approximation　and　the　genuine　solution　in　Sobolev　spaces　of　any　orders.　The　second　part　is　concerned　about　the　full　discrete　case,　in　which,　for　a　given　numerical　scheme　based　on　NGMs,　we　investigate　the　stability　and　error　estimate　respectively.　We　derive　the　stability　conditions　for　the　scheme　in　any　fractional　Sobolev　spaces.　Finally,　we　give　its　error　estimate　in　Hr　for　any　r　≥　0.