In this paper, we investigate curvature-adapted and proper complex equifocal
submanifolds in a symmetric space of non-compact type. The class of these submanifolds
contains principal orbits of Hermann type actions as homogeneous examples and is
included by that of curvature-adapted and isoparametric submanifolds with flat section.
First we introduce the notion of a focal point of non-Euclidean type on the ideal boundary
for a submanifold in a Hadamard manifold and give the equivalent condition for a
curvature-adapted and complex equifocal submanifold to be proper complex equifocal in
terms of this notion. Next we show that the complex Coxeter group associated with a
curvature-adapted and proper complex equifocal submanifold is the same type group as
one associated with a principal orbit of a Hermann type action and evaluate from above
the number of distinct principal curvatures of the submanifold.

Keywords: proper complex equifocal submanifold, Hermann type action,
complex Coxeter group