We report on the origin of the liquid-to-glass transition in a series of oligopeptides of γ-benzyl-L-glutamate up to the polymer (PBLG), and in Poly-Z-L-lysine (PZLL) and Polyglycine (PGly) using dielectric spectroscopy as a function of temperature and pressure. We show that temperature is the dominant control variable of the dynamics associated with the peptidic “glass transition.” This is an intrinsic feature of the peptide dynamics, irrespective of the type of amino acid and of the peptide secondary structure. The influence of the type of secondary structure (α helix vs β sheet) on the liquid-to-glass dynamics is discussed.