Secondary relaxations with properties closely related to the alpha-relaxation have fundamental importance in glass-forming substances including polymers. To distinguish these secondary relaxations from those involving intramolecular degrees of freedom, they are called the Johari-Goldstein (JG) beta-relaxations. Acting as the precursor of the alpha-relaxation, the JG beta-relaxation is supposedly ubiquitous in all glass-formers, a thesis supported by experiments on a variety of glass-formers. Notwithstanding, the JG beta-relaxation has not been identified definitively in the hydroxyl-terminated polypropylene glycols (PPGs) with various molecular weights, despite these polymers have been intensively studied experimentally in the last several decades. The difficulty of finding the JG beta-relaxation is due to the presence of a faster intramolecular gamma-relaxation and a slower relaxation originating from residual water. This is demonstrated in two recent papers by Gainaru et al. Macromolecules 2010, 43, 1907, and Kaminski et al. Macromolecules 2013, 46, 1973. In this paper, we show the presence of the JG beta-relaxation in the PPGs relaxation data by using the time honored criterion derived from the coupling model in conjunction with the observed anomalous temperature dependence of the gamma-relaxation caused by merging with the JG beta-relaxation, and new experimental data obtained by applying pressure on PPG4000 before and after drying the sample to remove the residual water. From the results, we conclude that the behavior of the PPGs is no different from the other glass-formers as far as the omnipresence of the JG beta-relaxation is concerned.