  This paper deals with the analysis of qualitative properties involved in the
dynamics of Keller-Segel type systems in which the diffusion mechanisms of the
cells are driven by porous-media flux-saturated phenomena. We study the
regularization inside the support of a solution with jump discontinuity at the
boundary of the support. We analyze the behavior of the size of the support and
blow--up of the solution, and the possible convergence in finite time towards a
Dirac mass in terms of the three constants of the system: the mass, the
flux--saturated characteristic speed, and the chemoattractant sensitivity
constant. These constants of motion also characterize the dynamics of regular
and singular traveling waves.
