This　article　provides　a　stability　analysis　for　the　backward　Euler　schemes　of　time　discretization　applied　to　the　spatially　discrete　spectral　standard　and　nonlinear　Galerkin　approximations　of　the　nonstationary　Navier-Stokes　equations　with　some　appropriate　assumption　of　the　data　(lambda,　u(o),　f).　If　the　backward　Enter　scheme　with　the　semi-implicit　nonlinear　terms　is　used,　the　spectral　standard　and　nonlinear　Galerkin　methods　are　uniform　stable　under　the　time　step　constraint　Deltat　less　than　or　equal　to　(2/lambdalambda(1)).　Moreover,　if　the　backward　Euler　scheme　with　the　explicit　nonlinear　terms　is　used,　the　spectral　standard　and　nonlinear　Galerkin　methods　are　uniform　stable　under　the　time　step　constraints　Deltat　=　O(lambda(n)(-1))　and　Deltat　=　O(lambda(m)(-1)),　respectively,　where　lambda(n)(-1)　less　than　or　equal　to　lambda(m)(-1),　which　shows　that　the　restriction　on　the　time　step　of　the　spectral　nonlinear　Galerkin　method　is　less　than　that　of　the　spectral　standard　Galerkin　method.　(C)　2004　Wiley　Periodicals,　Inc.