The dynamics of towed objects in a fluid environment is of interest for many practical situations. In this paper we report results for wake instabilities of spheres towed in a water tank. Six particles of different diameter and/or density ratio have been investigated, towed at 5 different constant velocities. The explored density ratios lay within Γ A ½1:06; 2:56, with particle Reynolds numbers Re p A ½100; 1200, corresponding to Galileo numbers in the range Ga A ½1300; 8000. We introduce a surrogate Galileo number Ga n that, by taking into account the towing force applied to the particle, allows a comparison with the case of free falling/ascending spheres. Using innovative 3D tracking techniques, the three-dimensional trajectory of each particle is reconstructed. The wake instability for the studied particles is found to be associated to a 3D helicoidal motion with an elliptical cross section in the plane perpendicular to the towing direction. The 3D oscillatory motion was found independent of the particle density ratio, with a threshold of the order of Re c p $ 355 (or Ga nc $ 245). This threshold is slightly larger than the one found for the free falling particles' transition to 3D chaotic motions (Re c p $ 310 or Ga c $ 225).