Nanofibers of a commercial styrene-butadiene-styrene triblock copolymer were electrospun from solution, and collected either as a nonwoven elastomeric fabric, or on a layer of graphite that was evaporated onto a glass microscope slide. The resulting nanofibers were elastic, birefringent, and most had diameters around 100 nm. A few thin, beaded fibers were found among the smooth nanofibers. The diameter of the fibers between the beads was as small as 3 nm. After staining with osmium tetroxide, the nanofibers were examined using transmission electron microscopy. Separated phases of styrene and butadiene blocks were observed. The single-phase domains were irregular in shape, but elongated along the axis of the fiber. Wide-angle X-ray diffraction patterns showed a weak indication of molecular orientation along the fiber axis, and the birefringence confirmed that such orientation was present. The single-phase domains grew larger in nanofibers that were held at room temperature (similar to 25 degrees C) for several days. Annealing at a temperature 70 degrees C greatly accelerated the growth of the single-phase domains. The nanofibers softened and flattened on the evaporated graphite during annealing.