The dynamics of coherent elliptic states in time-dependent electric and magnetic fields has been studied and it is shown that a linear Stark state may be transformed adiabatically into a circular Zeeman state through a continuous range of coherent elliptic states provided the fields vary slowly and are not parallel. The orientation vectors of the elliptic states rotate relative to the fields during the adiabatic transformation except when the fields are orthogonal. The condition for adiabatic behaviour is established for an easily realizable choice of field variation.