The proton magnetic relaxation times T-1 and T-2 of the three propionic acid species, HOOCC2D5, DOOCCH2-CD3, and DOOCCD2CH3, have been measured at a resonance frequency v = 12 MHz as a function of the temperature in the range 80 < T/K less than or equal to 270. 33 mol % DMSO-d(6) had to be added to the propionic acid in order to make measurements feasible in the supercooled region. T-1 measurements were performed at the frequencies v = 30 MHz and v = 48 MHz as well. Isotopic dilution experiments with constant content of propionic acid and varying degree of deuteration were made to obtain the intramolecular relaxation rates. The proton NMR spectra of the three propionic acid species were recorded at T = 130 K. From all these data, correlation times for the various proton-proton vectors were derived. It turned out that to each motion a slow and a fast mode contribution exists, however, the results are not compatible with the model of a molecule as a system of rigid bodies connected by axes about which rotation occurs. The various motional modes are described by continuous Cole-Davidson correlation time distributions. For all group time correlation functions g(t) of the second degree spherical harmonics after transcription in the Kohlrausch-Williams-Watts formalism are presented.