In cases of multi‐bunches operation in storage‐ring colliders, serious long‐range beam‐beam effects could be due to many parasitic collisions that are localized inside interaction regions or/and distributed around the ring. To reduce the long‐range beam‐beam effects, the compensation of long‐range beam‐beam interaction with magnetic multipole correctors based on minimizations of nonlinearities in one‐turn or sectional maps of a collider has been proposed. With LHC as a test model, the effectiveness of the multipole compensation of long‐range beam‐beam interactions was studied in terms of improvement of dynamic aperture and reduction of emittance growth. The study showed that both the local and global compensation of long‐range beam‐beam interactions with magnetic multipole correctors is very effective in increasing the dynamic aperture and improving the linearity of the phase‐space region relevant to the beams. © 2003 American Institute of Physics