Using isobaric-isothermal replica exchange molecular dynamics and the all-atom explicit water model, we examined the binding of FDDNP biomarkers to the A beta amyloid fibril fragment. Our results can be summarized as follows. First, FDDNP ligands bind with high affinity to the A beta fibril, and the hydrophobic effect together with pi-stacking interactions are the dominant factors governing FDDNP binding. In comparison, electrostatic interactions and hydrogen bonding play a minor role. Second, our simulations reveal a strong tendency of bound FDDNP molecules for self-aggregation. Accordingly, about two-thirds of all bound ligands form aggregated clusters of various sizes, and ligand-ligand interactions make considerable contribution to FDDNP binding. Third, FDDNP ligands bind to two distinct sites on the A beta fibril. Primary binding sites (NT) are located at the N-terminals of A beta 10-40 peptides, whereas secondary ones (CE) occur on the concave fibril edge near fibril channels. The NT sites are characterized by strong hydrophobic and pi-stacking interactions, favorable binding entropy resulting from multiple FDDNP binding orientations and propensity for self-aggregation but relatively weak van der Waals interactions. In contrast, the CE sites offer stronger van der Waals binding interactions but weaker hydrophobic and aromatic interactions and less favorable binding entropy. By comparing our data with previous studies, we suggest that the primary binding locations identified by us are likely to occur in other A beta fibril polymorphic structures. We also show that FDDNP binds via distinct mechanisms to A beta fibrils and monomers. We argue that FDDNP binds with stronger affinity to benign A beta monomers than to the fibrils, raising questions about the ability of FDDNP to selectively label amyloid deposits.