The role of two peptides, Aß₄₀ and Aß₄₂ in the early pathogenesis of the Alzheimer's disease (AD) is frequently emphasized in the literature. It is known that Aß₄₂ is more prone to aggregation than Aß₄₀, even though they only differ in two (I,A) amino acid residues at the C-terminal end. A direct comparison of the ensembles of conformations adopted by the monomers in solution has been limited by the inherent flexibility of the unfolded peptides. We characterize the conformations of Aß₄₂ and Aß₄₀ in water by using a combination of molecular dynamics (MD) and measured scalar ³J-coupling data. We perform replica exchange MD (REMD) simulations and find that various classical forcefields quantitatively reproduce the NMR data when the sampling is extended to the microseconds time scale. Using the quantitative agreement of the NMR data as a validation of the model, we proceed to compare the conformational ensembles of the Aß₄₂ and Aß₄₀ peptide monomers. Our analysis confirms the existence of structured regions within the otherwise flexible Aß peptides. We find that the C-terminus of Aß₄₂ is more structured than that of Aß₄₀. The formation of a ß-hairpin in the sequence ³¹IIGLMVGGVVIA involving short strands at residues 31-34 and 38-41 reduces the C-terminal flexibility of the Aß₄₂ peptide and may be responsible for the higher propensity of this peptide to form amyloids.