In this work, carbon nanofibers (CNF) synthesized by electrospinning are loaded with a combination of nickel and cobalt, both in the metallic and oxide forms (NiCo-loaded CNF), and studied as bifunctional air electrodes for metal-air batteries. The performance of the NiCo-loaded CNF sample is compared with a similarly prepared CoOCo/CNF catalyst both for oxygen reduction and evolution reactions. The combination of nickel and cobalt, both in metallic and oxide form, leads to a bifunctional catalyst with a half-wave potential for the ORR of 874 mV vs. RHE and a reversibility (ΔEOER-ORR) of 764 mV. The stability of the catalyst is assessed by means of a 24 h chronopotentiometric test at −80 mA cm−2 and charge-discharge cycles (30 min each) at ±20 mA cm−2. NiCo-loaded CNF shows a remarkable stability, maintaining a constant potential during both tests.