  We establish conditions when a certain type of the Riesz Decomposition
Property (RDP) holds in the lexicographic product of two po-groups. It is well
known that the resulting product is an $\ell$-group if and only if the first
one is linearly ordered and the second one is an $\ell$-group. This can be
equivalently studied as po-groups with a special type of the RDP. In the paper
we study three different types of RDP's. RDP's of the lexicographic products
are important for the study of pseudo effect algebras where infinitesimal
elements play an important role both for algebras as well as for the first
order logic of valid but not provable formulas.
