Abstract We show that the scattering operator carries a band in Hs(n) Hs1(n) into Hs(n) Hs1(n) for the sinh-Gordon equation and an analogous result also holds true for the nonlinear Schrdinger equation with an exponential nonlinearity, where sn/2 is arbitrary and n 2. Therefore, the scattering operators are infinitely smooth for the above two equations.