We introduce generalized pseudo-effect algebras as a
non-commu\-tative version of generalized effect algebras.

The importance of the algebras of the latter type in quantum physics
is based on the fact that they reflect the inner structure of
subsets of the positive cone of the group of self-adjoint operators
in a Hilbert space. The new algebras are designed to model subsets
of group cones as well; but now the underlying \pogr{} may be chosen
arbitrarily, in particular it does not need to be abelian.

We raise the question when a generalized pseudo-effect algebra is
actually representable in the positive cone of a \pogr{}. We are
able to give an affirmative answer for two special cases. Both times
a property of Riesz kind is involved, defined for our algebra in a
similar manner as known for \pogr{}s.
