  We investigate Andreev reflection at the interface between a superconductor
and a two--dimensional electron system (2DES) in an external magnetic field
such that cyclotron motion is important in the latter. A finite Zeeman
splitting in the 2DES and the presence of diamagnetic screening currents in the
superconductor are incorporated into a microscopic theory of Andreev edge
states, which is based on the Bogoliubov--de Gennes formalism. The
Andreev--reflection contribution to the interface conductance is calculated.
The effect of Zeeman splitting is most visible as a double--step feature in the
conductance through clean interfaces. Due to a screening current, conductance
steps are shifted to larger filling factors and the formation of Andreev edge
states is suppressed below a critical filling factor.
