  Proposed is a substantially simplified, Preisach-like model for
characterization of hysteretic systems, in particular magnetic systems. The
main idea is to replace a two-dimensional Preisach density with just two real
functions, describing in a {\em unique way} the reversible and irreversible
processes. As a byproduct of our model we prove, that the major hysteresis loop
alone is insufficient to produce the unique Preisach map. Keywords: magnetic
hysteresis; magnetization processes; materials testing; modeling.
