The relationship of structure and conductivity has been investigated in the Co substituted BIMEVOX system Bi2V1-xCoxO5.5-3x/2, 0.07 less than or equal to x less than or equal to 0.25 (BICOVOX). This system has been characterised using a.c. impedance spectroscopy, X-ray and neutron diffraction. The Arrhenius plots all show two straight line segments, one at low temperatures, below 450 degrees C, and one at high temperatures, above 550 degrees C. In the intermediate region, 3 types of behaviour are observed which appears to be composition dependent. All compositions showed differences in conductivity after the first heating cycle. However, this thermal hysteresis persisted in subsequent heating-cooling cycles only in compositions below x = 0.10. All BICOVOX samples in the composition range studied show essentially the tetragonal gamma-phase structure, with evidence for a superstructure modulation at low temperatures from the neutron data.