With the view of understanding the low frequency (40-50 cm(-1)) motional processes in L-alanine around 4 K, we have carried out heat capacity (C-P) and electron spin echo (ESE) measurements on L-alanine and L-alanine-d(7). The obtained C-P data show the so-called boson peak (seen as a maximum in C-P/T-3 versus T plots) in the low temperature region (1.8-20 K). The phase memory time, T-M, and spin lattice relaxation time, T-1, of the spin probe, the so-called first stable alanine radical (SAR1), (CHCH3COOH)-C-., have been measured between 4 and 105 K. The obtained relaxation rate 1/T-1 shows an anomalous increase which coincides with the emergence of a boson peak in the low temperature region (4-20 K). Together, the ESE and the C-P data confirm the existence of a thermally activated dynamic orientational disorder in the lattices of both compounds below 20 K. The results help explain the discrepancy between the C-P data from powders and single crystals of alanine, as well as the proanomalous relaxation mechanisms for SAR1 in these lattices, and they also provide a mechanism for the spin-lattice relaxation process for SAR1 at cryogenic temperatures. (C) 2004 American Institute of Physics.