The motion of an overhead trolley wire, suspended at equal intervals by stiff springs, in response to a pantograph moving with constant speed is analysed. The pantograph is modelled by two discrete masses connected by springs and dampers. Away from the supports the inertia and elasticity of the pantograph can be neglected and a simple solution for the wire and pantograph displacement is obtained. Near a support this solution is not valid as it predicts discontinuities in the vertical pantograph velocity. A different first approximation is then required in which the support elasticity and the pantograph inertia and elasticity must be included. This problem is reduced to that of solving a system of four linear differential equations containing one term with a stretched argument. The numerical and asymptotic solution of such a system is discussed and results are obtained for the contact force and pantograph displacement near a support in typical operating conditions. This disturbance at the support is propagated with the wire wave speed and reflected at the subsequent support, thus interacting with the pantograph again. This interaction is analysed and a uniformly valid solution obtained for the contact force over a complete span. Some conclusions are made about possible operating conditions in which loss of contact between the pantograph and the wire may occur.