We investigate the role of the radial orbit instability in the formati
on of galactic halos through dissipationless collapse. We present nume
rical simulations where both the Hubble expansion and the inhomogeneit
ies of the protogalactic material have been taken into account. We fin
d that the radial orbit instability is a transient effect for a wide v
ariety of initial conditions, including those with cosmological-like d
ensity fluctuations, as a result of the combination of two effects: th
e inhomogeneities give rise to condensations whose interactions introd
uce tangential motions, and the Hubble expansion delays the collapse l
ong enough for those motions to grow, preventing the instability. We c
onclude that, with reasonable initial conditions, the end product of a
dissipationless collapse does not need to be a triaxial system.