It is possible to classify the solid state catalyst systems into two categories; structure static catalyst and structure dynamic catalyst. The former is the catalyst in which the original structural circumstances of surface active center, such as coordinatively unsaturated state of active element, length and order of metal-ligand bond or of a bond between structural component, and their bond angle, are maintained unchanged during catalysis. The example is molybdenum sulfid which is a good catalyst for the isomerization and hydrogenation of olefins. On the contrary, the catalysts, in which the above circumstances of surface active center are changing dynamically during catalysis, are classified into the latter category. Molybdate catalysts for olefin oxidation by molecular oxygen at high temperature belong to this category. Main difference between two categories is whether the originally coordinated ligand on metal cation, such as sulfur anion of molybdenum sulfid and oxygen anion of metal molybdate, can participate in the catalysis directly or not. When the coordinated ligand is involved in the reaction, resulting abnormal coordinatively unsaturated state of surface active center must be sustained by the dynamic structure changes of both surface and bulk for the steady state catalysis. The bulk structure, therefore, affects strongly the properties of structure dynamic catalysts, whereas the properties of structure static catalysts depend on the surface structure like coner and edge mainly. The relationship between catalytic properties and structural stability of molybdate catalysts in the selective oxidation of propylene was discussed on the basis of 18O tracer study.