Numerically efficient Preisach-based vector hysteresis models for elli
psoidally magnetizable media are presented. Both models are based on o
rthogonal coupled scalar models and take into consideration the variat
ion in particle switching fields and interaction; however, the couplin
g mechanism is different in the two models. The rules determining the
magnetization state corresponding to the vector applied field are disc
ussed. The basic rotational remanence properties of the models are com
patible with observed vector phenomena.