La0.9Sr0.1Ga0.8Mg0.2O3-x+delta (LSGM) was additionally doped by y = 0.1-0.3 of the transition metals M = Cr, Mn, Fe, Co to form La0.9Sr0.1(Ga1-yMy)(0.8)Mg0.2O3-x+delta. After heating in air at 1400 degrees C single phase materials of the cubic perovskite type are obtained. Only the addition of Co y > 0.1 in oxidizing conditions (air) leads to a hexagonal structure. The dopants occupied the Ga-site of the perovskite structure. The oxygen stoichiometry range delta between the reduced and oxidized state of the mixed oxides were determined by solid electrolyte coulometry. The delta-values increase with increasing transition metal doping and in the row Cr, Mn, Fe, Co. An approach is given for the calculation of mean ionic radii, Goldschmidt tolerance factors and free volumes of mixed and nonstoichiometric oxides taking into account the real mole fractions and oxidation states of the cations. At the dopant concentration y = 0.1 the lattice parameter a increases from Co to Cr according to the mean ionic radii. The electrical conductivity of La0.9Sr0.1(Ga0.9M0.1)(0.8)Mg0.2O3-x+delta (M = Fe, Co) is of the ionic type. No break in the activation energy is observed, in opposition to the behaviour of LSGM near 600 degrees C. The A-substoichiometric La0.85Sr0.1(Ga0.9Co0.1)(0.8)Mg0.2O3-x+delta, has the highest ionic conductivity, at 600 degrees C twice as high as LSGM. At M-fractions y > 0.1, the conductivity increases due to additional p-type conduction.