Polymerization of the soluble beta-amyloid peptide into highly ordered fibrils is hypothesized to be a causative event in the development of Alzheimer's disease. Understanding the interactions of Abeta with inhibitors on an atomic level is fundamental for the development of diagnostics and therapeutic approaches, and can provide, in addition, important indirect information of the amyloid fibril structure. We have shown recently that trRDCs can be measured in solution state NMR for peptide ligands binding weakly to amyloid fibrils. We present here the structures for two inhibitor peptides, LPFFD and DPFFL, and their structural models bound to fibrillar Abeta(14-23) and Abeta(1-40) based on transferred nuclear Overhauser effect (trNOE) and transferred residual dipolar coupling (trRDC) data. In a first step, the inhibitor peptide structure is calculated on the basis of trNOE data; the trRDC data are then validated on the basis of the trNOE-derived structure using the program PALES. The orientation of the peptide inhibitors with respect to Abeta fibrils is obtained from trRDC data, assuming that Abeta fibrils orient such that the fibril axis is aligned in parallel with the magnetic field. The trRDC-derived alignment tensor of the peptide ligand is then used as a restraint for molecular dynamics docking studies. We find that the structure with the lowest rmsd value is in agreement with a model in which the inhibitor peptide binds to the long side of an amyloid fibril. Especially, we detect interactions involving the hydrophobic core, residues K16 and E22/D23 of the Abeta sequence. Structural differences are observed for binding of the inhibitor peptide to Abeta14-23 and Abeta1-40 fibrils, respectively, indicating different fibril structure. We expect this approach to be useful in the rational design of amyloid ligands with improved binding characteristics.