The frequency dependent optical and dielectric properties of boehmite (AlOOH) and ammonium aluminum carbonate hydroxide (AACH) nanostructures, prepared at different temperatures via hydrothermal synthesis, were studied by using terahertz time domain spectroscopy (THz-TDS). The complex refractive indices, absorption coefficients and complex dielectric constants were determined and compared for different synthesis temperatures. X-ray diffraction (XRD) and Fourier transform infrared spectroscopy (FTIR) were also performed to confirm the formation of boehmite and AACH. Scanning electron microscopy (SEM) was performed to study the morphology of nanostructures. The study reveals the formation of AACH at higher temperatures and decrease in refractive index with increasing synthesis temperature. The higher absorption coefficient and lower refractive index and dielectric constant were observed for AACH than for boehmite.