Control of surface wetting properties to produce strongly hydrophobic or hydrophilic effects is at the heart of many macro- and microfluidic applications. In this work, we have investigated coaxial electrospinning to produce core-sheath-structured nano/microfibers that combine different properties from individual core and sheath materials. Teflon AF is an amorphous fluoropolymer that is widely utilized as a hydrophobic material. Hydrophobic fluoropolymers are normally not electrospinnable because their low dielectric constant prevents sufficient charging for a solution to be electrospun. The first Teflon electrospun fibers are reported using coaxial electrospinning with Teflon AF sheath and poly(epsilon-caprolactone) (PCL) core materials. Using these core/sheath fibers, superhydrophobic and oleophobic membranes have been successfully produced. These coaxial fibers also preserve the core material properties as demonstrated with mechanical tensile tests. The fact that a normally nonelectrospinnable material such as Teflon AF has been successfully electrospun when combined with an electrospinnable core material indicates the potential of coaxial electrospinning to provide a new degree of freedom in terms of material combinations for many applications.