Long-term evolution of westward-travelling nonlocal modons on the β-plane, i.e. dipolar vortices imbedded in slowly damping Rossby wave fields, is studied numerically. In the framework of the nondivergent (barotropic) model, two stages of the evolution are observed. At the first stage (for about 30 synoptic periods), the parameters and the form of the vortex practically remain constant, whereas at the second stage, vorticity filaments are emitted. Due to the filamentation, the vortex core contracts, the potential vorticity peaks of the vortex pair get closer, and the modon speeds up. In the divergent (equivalent-barotropic) model, nonlocal modons and the Lamb modon (that has no wave field outside the dipolar core) evolve much more slowly, essentially preserving the initial shape and propagation speed until about 100 synoptic periods.