  Possible deviations from linearity of the LMC Cepheid PL and PLC relations
are investigated. Two datasets are studied, respectively from the OGLE and
MACHO projects. A nonparametric test, based on linear regression residuals,
suggests that neither PL relation is linear. If colour dependence is allowed
for then the MACHO PL relation is found to deviate more significantly from the
linear, while the OGLE PL relation is consistent with linearity. These finding
are confirmed by fitting "Generalised Additive Models" (nonparametric
regression functions) to the two datasets. Colour dependence is shown to be
nonlinear in both datasets, distinctly so in the case of the MACHO Cepheids. It
is also shown that there is interaction between the period and colour functions
in the MACHO data.
