  We discuss the classification of symmetries and the corresponding symmetry
groups in the two-Higgs-doublet model (THDM). We give an easily useable method
how to determine the symmetry class and corresponding symmetry group of a given
THDM Higgs potential. One of the symmetry classes corresponds to a Higgs
potential with several simultaneous generalised CP symmetries. Extending the CP
symmetry of this class to the Yukawa sector in a straightforward way, the
so-called maximally-CP-symmetric model (MCPM) is obtained. We study the
evolution of the quartic Higgs-potential parameters under a change of
renormalisation point. Finally we compute the so called oblique parameters S,
T, and U, in the MCPM and we identify large regions of viable parameter space
with respect to electroweak precision measurements. We present the
corresponding allowed regions for the masses of the physical Higgs bosons.
Reasonable ranges for these masses, up to several hundred GeV, are obtained
which should make the (extra) Higgs bosons detectable in LHC experiments.
