In this paper, we present results of dielectric and shear-mechanical studies for amine (2-ethyl-1-hexylamine) and thiol (2-ethyl-1-hexanethiol) derivatives of the monohydroxy alcohol, 2-ethyl-1-hexanol. The amine and thiol can form hydrogen bonds weaker in strength than those of the alcohol. The combination of dielectric and shear-mechanical data enables us to reveal the presence of a relaxation mode slower than the α-relaxation. This mode is analogous to the Debye mode seen in monohydroxy alcohols and demonstrates that supramolecular structures are present for systems with lower hydrogen bonding strength. We report some key features accompanying the decrease in the strength of the hydrogen bonding interactions on the relaxation dynamics close to the glass-transition. This includes changes (i) in the amplitude of the Debye and α-relaxations and (ii) the separation between primary and secondary modes.