The first is a hat badge for the Rheinland-Pfalz Polizei......
and the second is a hat badge for the Saarland Polizei.
These two hat badges date to the post-1975 era. They are attached to the hat with metal prongs.
Here are some photos of the Rheinland-Pfalz badge:
Here are some photos of the Saarland badge:
To finish things up, here are some archive photos from the original Polizei departments: