In this paper we have investigated the time-stationary solutions of weak double layers and solitary waves moving near the ion acoustic speed. It has been found that these nonlinear waves exist when the electric potential is negative and the reflected (trapped) ion density is very much depleted. Both cases of isothermal and nonisothermal electrons have been considered. It has been shown that the double layers and solitary waves discussed in this paper may explain the recent observations on the auroral field lines.