  We consider automorphisms of homogeneous parabolic geometries with a fixed
point. Parabolic geometries carry the distinguished distributions and we study
those automorphisms which enjoy natural actions on the distributions at the
fixed points. We describe the sets of such automorphisms on homogeneous
parabolic geometries in detail and classify, whether there are non--flat
homogeneous parabolic geometries carrying such automorphisms. We present two
general constructions of such geometries and we provide complete
classifications for the types (G,P) of the parabolic geometries that have G
simple and the automorphisms are of order 2.
