  A discussion of how to calculate asymptotic expansions for polyhomogeneous
spacetimes using the Newman-Penrose formalism is made. The existence of
logarithmic Newman-Penrose constants for a general polyhomogeneous spacetime
(i.e. a polyhomogeneous spacetime such that $\Psi_0=\O(r^{-3}\ln ^{N_3})$) is
addressed. It is found that these constants exist for the generic case.
