The partially Cu- or Ni-substituted compounds (Bi4V2(1-x)M2xO11-3x; M = Cu, Ni) are highly oxygen-conducting. Three phases (alpha, beta, gamma) are observed in the unsubstituted compound; alpha is the low-conducting room temperature phase and gamma the high-conducting phase at high temperature. Structure and conductivity are studied as a function of the substitution on the vanadium sites. Between 0 and 6% at room temperature, the Cu compound remains in the orthorhombic alpha phase and its ionic conductivity increases. A strong anisotropic conductivity is observed. For 0.07 less-than-or-equal-to x less-than-or-equal-to 0.12, the average structure is tetragonal (gamma-type) at room temperature. The conductivity is very high and does not vary very much over this substitution range. Impedance spectroscopy measurements have also been carried out on the x = 0.07 Ni-substituted compound. Commensurate or incommensurate superstructures are observed for all of these compounds.