  We define a parameter dependent notion of stability for principal bundles
with a certain local decoration, which generalizes both parabolic and level
structures, and construct their coarse moduli space. A necessary technical step
is the construction of the moduli space of tuples of vector bundles with a
global and a local decoration, which we call decorated tumps. We introduce a
notion of asymptotic stability for decorated tumps and show, that stable
decorated principal bundles can be described as asymptotically stable decorated
tumps.
