The nanofibers produced by electrospinning from a solution of a high-molecular copolymer of acrylonitrile with methyl methacrylate and itaconic acid are studied as electrically conducting material, which is applicable for the fabrication of biofuel cells (BFCs). In order to increase electrical conductivity, they are successively exposed to oxidative thermal stabilization in air and high-temperature vacuum treatment at 1500 and 2300-2550 degrees C. The structure of the materials is studied using various techniques including IR and Raman spectroscopy. As a result of the studies, the conditions of heat treatment that produce fiber materials with an acceptable defect level and sufficient electrical conductivity for microbial BFCs are determined.