A process using a niobium catalyst includes the step of reacting an ester or carboxylic acid with oxygen and an alcohol in the presence a niobium catalyst to respectively produce an .alpha.,.beta.-unsaturated ester or carboxylic acid. Methanol may be used as the alcohol, and the ester or carboxylic acid may be passed over the niobium catalyst in a vapor stream containing oxygen and methanol. Alternatively, the process using a niobium catalyst may involve the step of reacting an ester and oxygen in the presence the niobium catalyst to produce an .alpha.,.beta.-unsaturated carboxylic acid. In this case the ester may be a methyl ester. In either case, niobium oxide may be used as the niobium catalyst with the niobium oxide being present on a support. The support may be an oxide selected from the group consisting of silicon oxide, aluminum oxide, titanium oxide and mixtures thereof. The catalyst may be formed by reacting niobium fluoride with the oxide serving as the support. The niobium catalyst may contain elemental niobium within the range of 1 wt % to 70 wt %, and more preferably within the range of 10 wt % to 30 wt %. The process may be operated at a temperature from 150 to 450.degree. C. and preferably from 250 to 350.degree. C. The process may be operated at a pressure from 0.1 to 15 atm. absolute and preferably from 0.5-5 atm. absolute. The flow rate of reactants may be from 10 to 10,000 L/kg.sub.(cat) /h, and preferably from 100 to 1,000 L/kg.sub.(cat) /h.