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Development of practical applications of sources, detectors, convertors and other devices in terahertz (THz) range requires continues improvement of their functional properties and search for new materials. Nanostructured objects allowing introduce new properties to the bulk materials tailoring them for certain practical applications. Several works were devoted to the properties and practical use of porous silicon in THz range. In this work the optical properties of a novel material – nanostructured alumina oxyhydroxide (NOA) and some related nanocomposites were studied in THz range. NOA materials possess high specific surface ~300 m2/g with the structure consisting from alumina nanofibrils integrated into the 3D network. The refractive index n and absorption coefficient α of the NOA samples in THz range were measured by a standard pump-probe technique and evaluated using the Bruggeman effective medium approximation. Influence of the physically absorbed water on the fibrils’ surface on the n and α spectra was studied. THz spectra are shown to be sensitive to structural modifications of the samples – both phase transitions and presence of water on the fibrils’ surface.