The present invention features a method of making hydrous zirconium oxide having desirable properties, including resistance to moisture content, predetermined particle size, and developed porosity and surface area. The inventive material is suitable for use as an ion exchanger, a catalyst and a catalyst support. The process comprises providing a liquid comprising a zirconium compound and an alkali metal-containing reagent. The alkali metal-containing reagent may comprise a compound selected from the group consisting of MOH-M.sub.2SO.sub.4, MOH-M.sub.3PO.sub.4, and combinations thereof, where M is at least one of Li, Na and K. The zirconium compound may be treated with the alkali metal-containing reagent effective to form a mixture which achieves an uptake of alkali metal in an amount ranging from 0.5 to 2.5 meq/g. The mixture is reacted to form the hydrous zirconium oxide. A molar ratio of SO.sub.4/Zr and PO.sub.4/Zr in the mixture may range from 0.2-0.7:1. The mixture may be heated at a temperature ranging from 80 to 150.degree. C. to produce a reaction product. The reaction product may be treated with acid having a pH ranging from 4 to 8 at a temperature ranging from 20 to 60.degree. C. to form the hydrous zirconium oxide. Also featured is a method of making hydrous hafnium oxide. The inventive hydrous zirconium oxide and hydrous hafnium oxide are characterized by at least one of the following: stability against moisture loss, a particular surface area, a particular pore size distribution, an affinity towards anions including at least one of PO.sub.4, HPO.sub.4, H.sub.2PO.sub.4, AsO.sub.4, HAsO.sub.4, H.sub.2AsO.sub.4 and AsO.sub.3, oxoanions of Cr, Se, B, Mo,and W, and/or resistance against poisoning by SiO.sub.3 and SO.sub.4.