CNT's are expected to revolutionize a range of technologies because of their unique mechanical and electrical properties. Using nanotubes in structural materials holds significant promise due to their extremely high modulus and tensile strength, however their cost, production rate and integration into a fiber form severely limit the current structural application opportunities. We report the investigation of the formation of carbon nanotubes from a polymeric precursor using an electrospinning production process. This CNT formation concept is based upon modeling studies performed by Sinnot. Reactive Empirical Bond order calculations show that for small diameter carbon fibers, less than about 60 nm, the SWNT and MWNT phases are thermodynamically favored relative to an amorphous or planar graphitic nanofiber structure. We have developed a novel process using continuous electrospun polyacrylonitrile (PAN) nanofibers as precursors to continuous SWNT and MWNT. The process for converting PAN nanofibers to SWNT's and MWNT's follows the process for typical carbon fiber manufacture. The PAN nanofibers, of 10 to 100 nm in diameter, are crosslinked by heating in air and then decomposed to carbon via simple pyrolysis in inert atmosphere. The pyrolyzed carbon nanofibers are then annealed to form the more energetically favorable SWNT or MWNT phase, depending upon the precursor diameter. We will discuss the process and characterization data.