Molecular relaxation properties of sodium dodecylsulfate in aqueous solutions with surfactant concentrations between 0.009 and 0.4 mol/L have been studied using broadband ultrasonic spectrometry in the frequency range 0.1-2000 MHz. Ultrasonic excess attenuation characteristics were found that could be well represented by a sum of three relaxation terms, each one characterized by a discrete relaxation time. The low-frequency term with concentration-dependent relaxation time, tau(1), between 0.06 and 3.5 mu s is discussed in terms of the surfactant monomer exchange. The noticeable effect from the incomplete dissociation of the surfactant counter ions and the variation of the monomer concentration following thereby is discussed. The second relaxation term (0.9 <= tau(2) <= 2.5 ns) is assigned to the limited radial diffusion of monomers within the micelles, yielding a mean diffusion length of 0.5 nm, in correspondence to protrusions by four methyl groups. The high-frequency relaxation term (0.1 <= tau(3) <= 0.2 ns) reflects the structural isomerizations of the hydrocarbon chains in the micellar cores, largely resembling those of liquid alkanes.