  Within finite temperature field theory, we show that truncated
non-perturbative self-consistent Dyson resummation schemes can be renormalized
with local vacuum counterterms. For this the theory has to be renormalizable in
the usual sense and the self-consistent scheme must follow Baym's Phi-derivable
concept. Our BPHZ-renormalization scheme leads to renormalized self-consistent
equations of motion. At the same time the corresponding 2PI-generating
functional and the thermodynamic potential can be renormalized with the same
counterterms used for the equations of motion. This guarantees the standard
Phi-derivable properties like thermodynamic consistency and exact conservation
laws also for the renormalized approximation schemes. We give also a short
overview over symmetry properties of the various functions defined within the
2PI scheme for the case that the underlying classical field theory has a global
linearly realized symmetry.
