The interaction of H (D) atoms with clean and D (H) covered Cu(111) surfaces was studied with TDS and direct product detection methods. H (D) atoms exhibit an initial sticking coefficient of 0.22. Due to abstraction, the surface saturation coverage is achieved at Theta=0.34, significantly less than the half monolayer coverage obtained through exposure of energetic H-2 molecules to Cu(111) surfaces. Adsorbed H (D) desorbs recombinatively between 250 and 400 K. Desorption of absorbed H (D) via gaseous H-2(D-2) around 200 (210) K was observed according to a zero-order rate law with an activation energy of 0.40 (0.35) eV. Abstraction of D (H) by H (D) at 80 K lead to gaseous HD and D-2(H-2) formation. About 1% of the adsorbed species occurred in homonuclear products. Throughout the abstraction reaction the HD rate was found strictly proportional to coverage and flux, in line with a purely quasifirst-order, exponentially decreasing Eley-Rideal-type product rate. However, this phenomenology as well as the occurrence of homonuclear products can be explained by the exclusive action of hot-atom mechanisms, controlled by similar probabilities of reaction and sticking of hot atoms. The abstraction probabilities for adsorbed H or D, extrapolated to unity coverage, are 0.36 per incoming atom, the apparent abstraction cross-sections were obtained as sigma=2.0 A(2) for H (ad) and D (ad). Abstraction is independent of temperature. Absorbed species are not extracted by incoming atoms.