  The existence of conserved quantities with a structure similar to the
Newman-Penrose quantities in a polyhomogeneous space-time is addressed. The
most general form for the initial data formally consistent with the
polyhomogeneous setting is found. The subsequent study is done for those
polyhomogeneous space-times where the leading term of the shear contains no
logarithmic terms. It is found that for these space-times the original NP
quantities cease to be constants, but it is still possible to construct a set
of other 10 quantities that are constant. From these quantities it is possible
to obtain as a particular case a conserved quantity found by Chrusciel et al.
