Based on stellar evolution simulations, we demonstrate that rapidly accreting white dwarfs in close binary systems are an astrophysical site for the intermediate neutron-capture process. During recurrent and very strong He-shell flashes in the stable H-burning accretion regime H-rich material enters the He-shell flash convection zone.12 C(p, γ) 13 N reactions release enough energy to potentially impact convection, and i process is activated through the 13 C(α, n) 16 O reaction. The H-ingestion flash may not cause a split of the convection zone as it was seen in simulations of He-shell flashes in post-AGB and low-Z AGB stars. We estimate that for the production of first-peak heavy elements this site can be of similar importance for galactic chemical evolution as the s-process production by low-mass AGB stars. The He-shell flashes result in the expansion and, ultimately, ejection of the accreted and then i-process enriched material, via super-Eddington luminosity winds or Roche-lobe overflow. The white dwarf models do not retain any significant amount of the accreted mass, with a He retention efficiency of 10% depending on mass and convective boundary mixing assumptions. This makes the evolutionary path of such systems to supernova Ia explosion highly unlikely.