A systematic Raman-scattering investigation has been carried out on sol-gel alumina prepared by the hot-water hydrolysis and condensation of Al(${\mathrm{OC}}_{4}$${\mathrm{H}}_{9}$${)}_{3}$, the Yoldas process, as a function of process variables such as the time spent in the sol phase. Nanocrystalline boehmite, \ensuremath{\gamma}-AlO(OH), is the principal component of these materials. We have found small but systematic changes, as a function of sol aging time, in the line shape and position of the dominant boehmite Raman band observed in the alumina hydrogels. These spectral changes are interpreted in terms of nanocrystallinity-induced finite-size effects associated with the slow growth of AlO(OH) nanocrystals in the sol. X-ray-diffraction experiments were used to determine nanocrystal sizes (as small as 3 nm for gels prepared from fresh sols) and to estimate growth kinetics from the Raman-line-shape results. The Raman peak-position shift is proportional to ${\mathit{L}}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\alpha}}}$, where L is the average nanocrystal size and \ensuremath{\alpha} is a Raman-versus-size scaling exponent. For AlO(OH) we find \ensuremath{\alpha} to be 1.0, close to the scaling-exponent values reported for graphite and boron nitride (BN) and different from the values (about 1.5) that describe the reported behavior of Si and GaAs.