TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Catalyst: The catalyst has a surface area of more than 5 m2/g, and has higher selectivity at more than 100 psig compared with a catalyst or precursor of the catalyst in atmospheric pressure of 25 psig. The catalyst has a porous microstructure with a pore size of 10-1000 Angstrom, and comprises a cocatalyst including a metal chosen from vanadium, niobium, tantalum, chromium, molybdenum, tungsten, manganese, rhenium, iron, cobalt, nickel, copper, zinc, tin, lead, antimony and/or bismuth, preferably vanadium, niobium, tantalum, chromium, rhenium and/or iron, and alkali metal and/or alkaline earth metal.Preferred Conditions: The rare earth compound is treated with an organic acid to form an aqueous mixture with a pH of 2-6. The rare earth compound is a rare earth oxide, hydroxide, acetate, carbonate or nitrate, preferably an oxide. The treated rare earth compound is calcined at 400-800 degreesC in an atmosphere of flowing air. The cocatalyst and alkali metal and/or alkaline earth metal compound are added to the rare earth compound and/or catalyst precursor. The precursor is formed on or mixed with a support material.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Process: The lower hydrocarbon is methane. The organic acid is acetic acid, formic acid, propionic acid or butyric acid. The oxidative dehydrogenation is performed at a pressure of more than 100 psig and at less than 700 degreesC. Preferred Definitions:    A = 0.4-1.6;    M = lanthanum, praseodymium, neodymium, samarium or europium.    EXAMPLE - 8 g of lanthanum trioxide were mixed with 50 ml of deionized water, and the mixture was slowly heated with stirring to evaporate water, dried, calcined in air at 400 degreesC for 1 hour, pressed and broken into 14/30 mesh particles. The catalyst precursor with surface area of 13.9 m2/g obtained was placed in a reactor and pressurized to 125 psig with methane and oxygen in a ratio of 9:1 at a flow rate of 500 cc/minute and a gas hourly space velocity of 30000 per hour. The precursor was heated to 450 degreesC and held for 4 hours during which time reaction occurred with low oxygen conversion. The temperature was then repeatedly raised by 50 degreesC increments and held for 4 hours up to 700 degreesC. The catalyst had 2C and 3C selectivity (in %) of 0, 46, 46, 39-32, 2, and 2 at 450 degreesC, 500 degreesC, 550 degreesC, 600 degreesC, 650 degreesC and 700 degreesC, respectively; methane conversion (in %) of 0.3, 10, 9, 8, 5, and 5 at 450 degreesC, 500 degreesC, 550 degreesC, 600 degreesC, 650 degreesC and 700 degreesC respectively; and oxygen conversion of 6, 100, 100, 100, 100 and 100 at 450 degreesC, 500 degreesC, 550 degreesC, 600 degreesC, 650 degreesC and 700 degreesC, respectively. The catalyst had stable selectivity at 500-550 degreesC.