During the past decade, many electrical transmission tower structures have failed during downburst events. This study is a part of a research program aimed to understand the behaviour of transmission lines under such localized wind events. The present study focuses on the assessment of the dynamic behaviour of the line conductors under downburst loading. A non-linear numerical model, accounting for large deformations and the effect of pretension loading, is developed and used to predict the natural frequencies and mode shapes of conductors at various loading stages. A turbulence signal is extracted from a set of full-scale data. It is added to the mean component of the downburst wind field previously evaluated from a CFD analysis. Dynamic analysis is performed using various downburst configurations. The study reveals that the response is affected by the background component, while the resonant component turns to be negligible due large aerodynamic damping of the conductors.