  We discuss the renormalizability of Phi-derivable approximations in scalar
phi^4 theory in four dimensions. The formalism leads to self-consistent
equations for the 2-point and the 4-point functions which are plagued by
ultraviolet divergences. Through a detailed analysis of the one and two-loop
self-energy skeletons, we show that both equations can be renormalized
simultaneously and determine the corresponding counterterms. These insure the
elimination of ultraviolet divergences both at zero and finite temperature.
