This paper describes a nonlinear Image-Based Visual Servo (IBVS) controller for tracking nonlinear parallel 2-D curves, such as catenaries, with a fixed-wing aircraft. Image features are exploited from the image of the lines to design a feedback controller for the automatic manoeuvre. For curves in the vertical plane the proposed solution guarantees exponential stability in the horizontal direction and ultimate boundedness in the vertical direction, with bound proportional to the slope deviation with respect to a straight line. Simulation results are presented to illustrate the performance of the control approach.