Proton conduction of the La(III)M(III) compounds, LaM(ox)3·10H2O (abbreviated to LaM; M = Cr, Co, Ru, La; ox(2-) = oxalate) is studied in view of their networks. LaCr and LaCo have a ladder structure, and the ladders are woven to form a channel network. LaRu and LaLa have a honeycomb sheet structure, and the sheets are combined to form a layer network. The occurrence of these structures is explained by the rigidness versus flexibility of [M(ox)3](3-) in the framework with large La(III). The channel networks of LaCr and LaCo show a remarkably high proton conductivity, in the range from 1 × 10(-6) to 1 × 10(-5) S cm(-1) over 40-95% relative humidity (RH) at 298 K, whereas the layer networks of LaCr and LaCo show a lower proton conductivity, ∼3 × 10(-8) S cm(-1) (40-95% RH, 298 K). Activation energy measurements demonstrate that the channels filled with water molecules serve as efficient pathways for proton transport. LaCo was gradually converted to La(III)Co(II)(ox)2.5·4H2O, which had no channel structure and exhibited a low proton conductivity of less than 1 × 10(-10) S cm(-1). The conduction-network correlation of LaCo(ox)2.5·4H2O is reported.