Postprint version. Published in Topology and its Applications, Volume 56, Issue 2, March 14, 1994, pages 99-104.
The definitive version is available at https://doi.org/10.1016/0166-8641(94)90011-6.
We give a quantifier free characterization of realcompactness and ordered realcompactness in terms of monads. We also present simple proofs of some topological facts concerning realcompact spaces.