Continuous fibers are described having concentric layer or aligned sphere microphase-separated, styrene-isoprene block copolymer morphologies. The fibers are obtained by a two-fluid coaxial electrospinning technique in which the desired block copolymer is encapsulated as the core component within a polymer shell having a high glass transition temperature (T-g). The fibers range in diameter from 300 to 800 nm, and the block copolymer core ranges from 50 to 500 nm. Subsequent annealing of the fibers above the upper T-g of the block copolymer but below the T-g of the shell polymer results in microphase separation of the block copolymer under cylindrical confinement. The resulting fibers exhibit improved long-range order. This two-step strategy creates the opportunity to fabricate continuous nanofibers with periodic internal structure.