The leaky dielectric model (LDM) was extended to large droplet distortions in de electric fields. The resulting extended LDM (ELDM) reduces to the LDM for small droplet aspect ratios and to the pure dielectric model when the ratio of droplet and matrix conductivities equals the inverse ratio of their permittivities. The ELDM distinguishes between two types of phenomena possible at high electric fields: continuous deformation and hysteresis. For droplets deforming parallel to the electric field, the relationship that distinguishes between the two phenomena is a function of the droplet and matrix conductivities and viscosities but not of their permittivities. For droplets deforming perpendicular to the electric field, the relationship is a function of the droplet permittivities and conductivities but depends only slightly on the ratio of their viscosities. Some of the predictions of the LDM and the ELDM were compared with our own data and with data from the literature. For the systems that deformed parallel to the field direction,the ELDM not only predicted the data qualitatively but also predicted the data quantitatively when the experimental errors in its input parameters were taken into account, whereas the older LDM did not even predict the qualitative trend of the data. For the systems that deformed perpendicular to the field direction, however, the ELDM predicted the observed the aspect ratios in only one out of the four systems examined. In the other three systems, the LDM appeared to give reasonable predictions when either the ratio of the matrix/droplet viscosities was relatively small or the value of total charge relaxation time was relatively large. Thus, the applicability of the ELDM, as presently formulated, appears to be limited in the case of deformations perpendicular to the electric field.