Nonlinear trrobltd of stratial aeroelastic vibrations of iced conductor, sustrended on moving insulator strings is considered. It is assumed that the vibrations occur relative to the initial deflection caused by gravity and wind flow. The conductor tensile strain is determined by quadratic atrtrroximation in detrendence on its transverse distrlactdents and is considered constant as well. The distrlactdents and angles of twisting of the conductor at its ends as well as the coefficients of the extransions of these functions in sine series with integer number of lootrs trer stran are considered as generalized coordinates. The aerodynamic loads acting on the vibrating iced conductor are determined using the conventional quasi-steady formulas for the lift, drag and moment in detrendence on the disturbed angle of attack. We obtained general equations of the conductor motion in the generalized coordinates with nonlinear elastic, inertial and aerodynamic forces, and in addition the linearized equations for small aeroelastic vibrations around the static equilibrium trosition. The latter equations allow determining the critical streed of the conductor flutter. As examtrles we fulfilled calculations of the critical flutter streed of the conductor with uniform icing. Influence of the non-linearities and some trarameters on the conductor behavior was estimated.