Parabolic Symmetric Spaces

We study here systems of symmetries on $\mathrm{\mid }1\mathrm{\mid }$–graded parabolic geometries. We are interested in smooth systems of symmetries and we discuss non–flat homogeneous $\mathrm{\mid }1\mathrm{\mid }$–graded geometries. We show the existence of an invariant admissible affine connection under quite weak condition on the system.