  In this paper we confirm the existence of period-luminosity (PL) and
period-luminosity-colour (PLC) relations at maximum light for O and C Mira
variables in the LMC. We demonstrate that in the J and H bands the maximum
light PL relations have a significantly smaller dispersion than their
counterparts at mean light, while the K band and bolometric PL relations have a
dispersion comparable to that at mean light. In the J, H and K bands the fitted
PL relations for the O Miras are found to have smaller dispersion than those
for the C Miras, at both mean and maximum light, while the converse is true for
the relations based on bolometric magnitudes. The inclusion of a non-zero log
period term is found to be highly significant in all cases except that of the C
Miras in the J band, for which the data are found to be consistent with having
constant absolute magnitude. This suggests the possibility of employing C Miras
as standard candles.
  We suggest both a theoretical justification for the existence of Mira PL
relations at maximum light and a possible explanation of why these relations
should have a smaller dispersion than at mean light. The existence of such
maximum light relations offers the possibility of extending the range and
improving the accuracy of the Mira distance scale to Galactic globular clusters
and to other galaxies.
