Nanofibers of polymers were electrospun by creating an electrically charged jet of polymer solution at a pendent droplet. After the jet flowed away from the droplet in a nearly straight line, it bent into a complex path and other changes in shape occurred, during which electrical forces stretched and thinned it by very large ratios. After the solvent evaporated, birefringent nanofibers were left. In this article the reasons for the instability are analyzed and explained using a mathematical model. The rheological complexity of the polymer solution is included, which allows consideration of viscoelastic jets. It is shown that the longitudinal stress caused by the external electric field acting on the charge carried by the jet stabilized the straight jet for some distance. Then a lateral perturbation grew in response to the repulsive forces between adjacent elements of charge carried by the jet. The motion of segments of the jet grew rapidly into an electrically driven bending instability. The three-dimensional paths of continuous jets were calculated, both in the nearly straight region where the instability grew slowly and in the region where the bending dominated the path of the jet. The mathematical model provides a reasonable representation of the experimental data, particularly of the jet paths determined from high speed videographic observations. (C) 2000 American Institute of Physics. [S0021-8979(00)03609-4].