Abstract : This work is devoted to experimental and theoretical study of the behavior of water droplets (instability, deformation, coalescence), located on the surface of a high voltage composite insulator, in presence of electric field. The deformation of droplets is investigated according to several parameters such as volume, number and conductivity of the droplets as well as their positions with respect to the electrodes. A particular interest is focused on the electric charge accumulated on the droplet surface. The droplet influences on the electric field distribution as well as the amplification factor of the electric field are studied by a numerical method. A mathematical formulation of the deformation of water droplet located on a surface of insulator is developed. The mechanisms as well as parameters involved in coalescence of a pair of water droplets under the electric field stress are also investigated. A mathematical model is developed for analyzing the coalescence of a pair of water droplets sitting on the surface of an insulator in presence of the electric field. It is based on a diffuse interface model that essentially consists of a coupling between Navier-Stokes equations, the computing of electric force and a Cahn-Hilliard type equation describing the interface evolution including capillary phenomena. The approach followed and the results presented in this work open several perspectives as well from an experimental point of view as from a point of view of modeling and numerical simulation of physical phenomena affecting insulators of high voltage transport and distribution lines in humidity conditions (rain, dew...).