NOVELTY - Providing transition aluminas and precursor hydrated aluminas which are mesoporous, and are economical and relatively easy to perform.    USE - The mesostructured crystalline hydrated alumina composition is used as catalyst or catalyst supports in chemical processes, including the cracking, hydrocracking and hydrodesulfurization of petroleum, the steam reforming of hydrocarbon feed stocks ranging from natural gas to heavy naphthas to produce hydrogen, the synthesis of ammonia, and the control automobile exhaust emissions. It can also be used as absorbents. It is particularly used for converting a first liquid or gas stream to a second liquid or gas stream (claimed).    ADVANTAGE - The inventive mesostructured transition alumina composition is economical and easy to produce. It has textural properties, which are superior and more useful in catalytic and adsorption applications in comparison to bulk transition aluminas or bulk hydrated aluminas that lack a mesostructured framework.    DETAILED DESCRIPTION - Mesostructured crystalline hydrated alumina composition exhibits at least one low angle x-ray diffraction line corresponding to a lattice spacing of at least 2 nm and wide angle x-ray diffraction lines with copper potassium alpha radiation, where lambda is 0.1541 nm corresponding to an ordered lattice composed of oxygen atoms and hydroxide groups with aluminum in interstitial positions within the lattice. The surface area is at least 200 m2/g and the pore volume is at least 0.4 cm3/g.    INDEPENDENT CLAIMS are included for the following:    (a) a process for the preparation of a mesostructured hydrated alumina-organic modifier composite, which comprises reacting an alumina precursor including aluminum salts, oligomeric oxyhydroxyaluminum cations, non-ionic aluminum molecules, or their mixtures in solution with hydroxide ions in the presence of an organic modifier at 0-200degrees C for a period to cause crystallization; and filtering, washing, and drying the product;and    (b) process for converting a first liquid or gas stream to a second liquid or gas stream using a catalyst, which comprises using as the catalyst or catalyst component the inventive mesostructured crystalline hydrated alumina composition.