There are many technical situations, such as various biological or medical applications, in which a hydrophobic fluid must be encapsulated inside a hydrophilic polymer shell in the form of tiny microscopic pieces. A novel approach is presented, based on the co-electrospinning of the hydrophilic polymer melt (outside) and the hydrophobic fluid (inside), which results in beaded micro- and nanofibers, such that the hydrophobic fluid is efficiently encapsulated inside the beads. For the selected fluid couple, the low liquid-liquid surface tension and the high viscosity of the melt prevent the varicose break-up of inner fluid in the coaxial electrified jet until the very end of the co-electrospinning process. The resulting fibers present beads filled with the hydrophobic fluid, separated by a rather uniform distance whose length depends partially on the melt flow rate. The bead diameter grows with the inner flow rate, going from a monosized to a bisized distribution. In the case under study, the maximum relative (inner-to-outer) flow rate is one. The diameter of the solid fibers between beads scales well with existing theories for simple electrospinning.