Solid oxide fuel cells (SOFCs) offer the advantages of (i) employing less expensive catalysts compared to the expensive Pt catalyst used in proton exchange membrane fuel cells and (ii) directly using hydrocarbon fuels without requiring external fuel reforming due to the high operating temperature. However, the conventional high operating temperatures of 800 - 1000 °C lead to interfacial reactions and thermal expansion mismatch among the components and limitations in the choice of electrode and interconnect materials. These problems have prompted a lowering of the operating temperature to an intermediate range of 500 - 800 °C, but the poor oxygen reduction reaction kinetics of the conventional La[subscript 1-x]Sr[subscript x]MnO₃ perovskite cathode remains a major obstacle for the intermediate temperature SOFC. In this regard, cobalt-containing oxides with perovskite or perovskite-related structures have been widely investigated, but they suffer from large thermal expansion coefficient (TEC) mismatch with the electrolytes. With an aim to lower the TEC and maximize the electrochemical performance, this dissertation focuses on perovskite-related and trigonal RBaCo₄O₇-based oxide cathode materials. First, the effect of M = Fe and Cu in the perovskite-related layered LnBaCo₂₋xMxO₊[delta] (Ln = Nd and Gd) oxides has been investigated. The Fe and Cu substitutions lower the polarization resistance and offer fuel cell performance comparable to that of La[subscript 1-x]Sr[subscript x]CoO₃₋[delta] perovskite due to improved chemical stability with the electrolyte and a better matching of the TEC with those of standard electrolytes. Second, the perovskite-related intergrowth oxides Ln(Sr,Ca)₃Fe₁.₅Co₁.₅O₀ and La₁.₈₅Sr₁.₁₅Cu[subscript 2-x]Co[subscript x]O[subscript 6 +delta] and their composites with gadolinia-doped ceria (GDC) have been investigated. The electrical conductivity, TEC, and catalytic activity increase with increasing Co content. The composite cathodes exhibit enhanced electrochemical performance due to lower TEC and increased triple-phase boundary. Third, RBa(Co,Zn)₄O₇ (R = Y, Ca, and In) oxides with a trigonal structure and tetrahedral-site Con+ ions have been investigated. The chemical instability normally encountered with this class of oxides has been overcome by appropriate cationic substitutions as in (Y₀.₅Ca₀.₅)Ba(Co₂.₅Zn₁.₅)O₇ and (Y₀.₅In₀.₅)BaCo₃ZnO₇. With an ideal matching of TEC with those of standard electrolytes, the RBa(Co,Zn)₄O₇ (R = Y, Ca, and In) + GDC composite cathodes exhibit low polarization resistance and electrochemical performance comparable to that of perovskite oxides. / text