The frequency and temperature dependences of the ac conductivity and dielectric constant of the V 2 O 5 -MnO-TeO 2 system, containing two transition-metal ions, have been measured. The dc conductivity † dc measured in the high-temperature range decreases with addition of the oxide MnO. This is considered to be due to the formation of bonds such as V--O--Mn and Mn--O--Mn in the glass. The conductivity arises mainly from polaron hopping between V 4+ and V 5+ ions. It is found (...) that a mechanism of adiabatic small-polaron hopping is the most appropriate conduction model for these glasses. This is in sharp contrast with the behaviour of the Mn-free V 2 O 5 -TeO 2 glass, in which non-adiabatic hopping takes place. High-temperature conductivity data satisfy Mott's small-polaron hopping model and also a model proposed by Schnakenberg in 1968. A power-law behaviour † ac = A y s , with s < 1) is well exhibited by the ac conductivity † ac data of these glasses. Analysis of dielectric data indicates a Debye-type relaxation behaviour with a distribution of relaxation times. The MnO-concentration-dependent † ac data follow an overlapping large-polaron tunnelling model over the entire range of temperatures studied. The estimated model parameters are reasonable and consistent with changes in composition. (shrink)