This thesis is devoted to the study of the structure and relaxation dynamics in some oxygen ion conducting materials. Oxide based electrolytes and cathode/anode materials or fast oxide ion conductors have considerable applications in solid oxide fuel cell, oxygen gas sensors and solid state based devices. Some crystallographic families have shown high oxygenion mobility. Recent study on lanthanum molybdenum oxide (LAMOX), strontium and magnesium doped lanthanum gallate (LSGM) and doped yttria stabilized zirconia (YSZ) compounds have indicated their high applicability in intermediate temperature (600 - 800 C) solid oxide fuel cell (IT-SOFC). The structure and ion dynamics of doped La2Mo2O9 ceramic compounds have been studied in detail. The c...