  We study a broad class of asymmetric copulas introduced by Liebscher (2008)
as a combination of multiple - usually symmetric - copulas. The main thrust of
the paper is to provide new theoretical properties including exact tail
dependence expressions and stability properties. A subclass of Liebscher
copulas obtained by combining Fr\'echet copulas is studied in more details. We
establish further dependence properties for copulas of this class and show that
they are characterized by an arbitrary number of singular components.
Furthermore, we introduce a novel iterative representation for general
Liebscher copulas which de facto insures uniform margins, thus relaxing a
constraint of Liebscher's original construction. Besides, we show that this
iterative construction proves useful for inference by developing an Approximate
Bayesian computation sampling scheme. This inferential procedure is
demonstrated on simulated data.
