The dielectric relaxation of two long-chain glass forming monohydroxy alcohols, 2-butyl-1-octanol and 2-hexyl-1-decanol, is studied at low temperature. Remarkable broadening from the pure Debye relaxation is identified for the slowest dynamics, differing from the dielectric spectra of short-chain alcohols. The broadening of the Debye-like relaxation in the two liquids develops as temperature increases, and the approaching of the Debye-like and structural relaxation widths is shown. Similar results are observed in the dielectric spectra of dilute 2-ethyl-1-hexanol in either 2-hexyl-1-decanol or squalane. The results of the liquids and mixtures reveal a correlation between the broadening and the Debye-like relaxation strength. Molecular associations in monohydroxy alcohols are discussed with the modification of the Debye relaxation.