A self-consistent model was developed to study the stochastic acceleration (second-order Fermi) of interstellar pickup ions in the quiet solar wind (SW) and inside corotating merged interaction regions (CMIRs) in the presence of the effects of wave coupling and the damping of magnetohydrodynamic waves by pickup ions. Our simulations of the solar wind wave spectrum show that (1) Pickup H+ is mainly responsible for wave damping at large wave numbers with pickup He+ contributing very little and pickup O+ contributing nothing. (2) Strong wave-wave interactions wash out wave-damping effects for radial distances r≤10 AU from the Sun in the quiet solar wind and for r≤23 AU inside corotating merged interaction regions. This is to be contrasted with previous work which calculated strong wave damping inside 10 AU from the Sun in the absence of wave coupling. For the simulated pickup ion spectra the main results are as follows: (1) The pickup He+ and O+ spectra are unaffected by the wave damping. (2) In contrast, the accelerated pickup H+ spectra have concave features for kinetic energies 1--5 KeV which become more pronounced with increasing radial distance. This suppression of the pickup H+ acceleration is attributed to the wave damping caused by the pickup H+. (3) Inside corotating merged interaction regions the preacceleration of pickup ions is stronger because of the enhanced heliospheric magnetic field. The suppression of pickup H+ acceleration is smaller and only starts to show for r>23 AU. (4) Under the assumption that the seed population of anomalous cosmic rays should have speeds &ngr;>400 km s-1 the H+/He+ density ratio in this population can be as low as ~2.6 in the quiet solar wind and ~13 inside corotating merged interaction regions. Compared with the observed ratio of ~6 for anomalous cosmic rays (ACRs), our conclusion is that if CMIR and quiet SW regions are considered together, then the observed under abundance in ACR H+ could in principle be produced on average. ¿ 1998 American Geophysical Union