Inclusion complexes (ICs) composed of alpha-cyclodextrin (alpha-CD) and poly(D,L-lactic acid) (PDLLA), with 10/24 (IC1) and 15/46 (IC2) (% w/w) of PDLLA incorporated/initial PDLLA weight percentage, were prepared and characterized mainly by dielectric relaxation spectroscopy (DRS). Bulk PDLLA was also analyzed for comparison. DRS was revealed to be a suitable tool to distinguish the dynamical response of the PDLLA regions constrained in between alpha-CD channels from the fraction incorporated inside channels. While the cooperative alpha-process undergoes a dramatic depletion shifting to higher temperatures (similar to 4.5 degrees C) for the PDLLA interchannels portion, it is suppressed for PDLLA chains inside pores. It was demonstrated that the broad secondary relaxation of bulk PDLLA is the Johari-Goldstein process (beta(JG)-process). The detection of its analogue in the ICs at higher frequencies, to a greater extent in IC1, is interpreted as a true confinement effect where the dimensions of the alpha-CD channels interfere with the length scale of the beta(JG)-process. The limit predicted in the framework of the coupling model, where the alpha-relaxation transforms in the beta(JG)-process, seems to be reached in the ICs. Furthermore, it was found that the length scale of the additional gamma process only detected in the ICs is inferior to inter- or intrachannel dimensions.