  Perfect fluid spacetimes admitting a kinematic self-similarity of infinite
type are investigated. In the case of plane, spherically or hyperbolically
symmetric space-times the field equations reduce to a system of autonomous
ordinary differential equations. The qualitative properties of solutions of
this system of equations, and in particular their asymptotic behavior, are
studied. Special cases, including some of the invariant sets and the geodesic
case, are examined in detail and the exact solutions are provided. The class of
solutions exhibiting physical self-similarity are found to play an important
role in describing the asymptotic behavior of the infinite kinematic
self-similar models.
