  We study generalised P and CP transformations in the three-Higgs-doublet
model (3HDM) with Higgs and gauge fields only. We find that there are two
equivalence classes, with respect to flavour transformations, of generalised P
transformations and there is only one class of CP transformations. We discuss
the conditions the potential has to satisfy in order to be invariant under
these transformations. We apply the method of bilinears which we briefly
review. We discuss the relation to the conventional basis, where the potential
is written in terms of scalar products of the doublet fields. In particular we
reproduce the known result that a potential is invariant under CP
transformations if and only if there is a conventional basis where all
parameters are real. Eventually we study standard P and CP transformations in
the $n$-Higgs-doublet model (nHDM). We show that for the bilinears of the nHDM
the standard CP transformation corresponds to a diagonal linear transformation
with only $\pm 1$ as diagonal elements. We give this matrix explicitly for
arbitrary $n$.
