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The dynamics of towed objects in a fluid environment is of interest for many practical situations. We investigate experimentally the equilibrium and stability of the trajectory of a sphere towed at constant velocity at the tip of a cable with an unprecedented large length-to-diameter aspect ratio, exceeding 10 ^4 . The towing configuration is artificially obtained by considering a steady cable (with one fixed end and a free end to which a sphere is eventually attached) in a low-turbulence wind tunnel. We consider three different configurations: (i) the cable towed by itself; (ii) a light millimetric towed sphere made of expanded polystyrene; and (iii) a denser millimetric towed sphere made of lead. The trajectory of the cable tip is monitored using high-speed Lagrangian tracking, which allows one to characterize the average position and the dynamical fluctuations of the towed object. We show that the mean equilibrium position is well predicted by a simple model including the aerodynamical forces acting along the cable and on the towed sphere (when present). Concerning stability issues, we find that the heavy lead particle is always towed in stable conditions (within the accessible range of velocities) with only very low energy oscillations related to a weak pendulum-like motion. In contrast, the free end and light sphere cases are shown to become unstable when the towing velocity exceeds a certain threshold. Spectral analysis shows a flutter -type instability for the sphere, with a dominant oscillatory motion, while the cable alone develops a divergence -type instability with random fluctuations.