First, we have ensured that spherical nonrotating collisionless systems collapse while almost retaining spherical configurations during the initial contraction phases, even if they are allowed to collapse three-dimensionally. Next, based on the assumption of spherical symmetry, we examine the evolution of the velocity dispersions with collapse for those systems having uniform or power-law density profiles with Maxwellian velocity distributions by directly integrating the collisionless Boltzmann equation. The results show that as far as the initial contraction phases are concerned, the radial velocity dispersion never grows faster than the tangential velocity dispersion, except at small radii, where the nearly isothermal nature remains, irrespective of the density profiles and virial ratios. This implies that the velocity anisotropy as an initial condition should be a poor indicator of the radial orbit instability. The growing behavior of the velocity dispersions is briefly discussed from the viewpoint that phase-space density is conserved in collisionless systems.

Key words: Galaxies: formation --- Galaxies: structure --- Instabilities --- Methods: numerical --- Stellar dynamics