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Motion of a weakly conductive viscous jet accelerated by an external electric field is considered. Nonlinear rheological constitutive equation applicable for polymer fluids (Oswald–deWaele law) is applied. A differential equation for the variation of jet radius with axial coordinate is derived. Asymptotic variation of the jet radius at large distances from the jet origin is analyzed. It is found that the well-known power-law asymptote for Newtonian fluids with the exponent 1/4 holds for more general class of fluids, i.e., pseudoplastic (shear thinning) and dilatant (shear thickening) fluids with the flow index between 0 and 2. Dilatant fluids with the flow index greater than 2 exhibit power-law asymptotes with the exponents depending on the flow index. Results can be applied for the analysis of viscous polymer jets in the electrospinning process.