We have measured the dielectric relaxation of the glass-former 1-propanol for temperatures between 65 and 350 K in the frequency range 10(-2) to 2 . 10(10) Hz and the photon correlation spectroscopy decays near T-g. Attributing the strong Debye-type process of I-propanol to distinct -OH group effects leaves two faster processes related to the structural relaxation which can be identified as alpha-relaxation and Johari-Goldstein type beta-relaxation characteristic of nonhydrogen-bonding supercooled liquids. From the temperature dependent relaxation times tau(T) regarding the three distinct loss peaks, we can specify an alpha-beta-bifurcation temperature T-beta, which coincides with characteristic qualitative changes in the tau(T) behavior, as also observed for ortho-terphenyl and other glass-forming liquids. This assignment is confirmed by the correlation times derived from incoherent quasielastic light-scattering data obtained from the simultaneously measured photon-correlation spectroscopy.