We present a new model of the Jovian magnetospheric field which couples the internal field spherical harmonic coefficients from the Goddard Space Flight Center O6 model with an Euler potential formulation of the external field. The effects of the hinging and the delay of the Jovian current sheet and the sweep-back of the field lines resulting from the subcorotation of plasma in the magnetosphere are incorporated self-consistently into the Euler potential equations. Because Jovian magnetosphere undergoes substantial temporal changes in its configuration, it was found necessary to obtain different fit parameters for each of the outbound passes of Pioneer 10, Voyager 1, and Voyager 2. A detailed comparison of the model with the observations obtained in the nightside Jovian magnetosphere reveals that the Euler potential approach can be used successfully to represent the field of external origin in the Jovian magnetosphere. The proposed models are applicable to the inner magnetosphere at all local times and to the middle and the outer magnetosphere on the nightside. The models should provide reliable magnetic field predicts along the trajectory of Galileo in all 11 of the initially planned orbits. We also discuss further extensions of the model which would extend their applicability to all local times and radial distances.¿ 1997 American Geophysical Union