Complex chromosome aberrations are characteristically induced after exposure to low doses of densely ionising radiation, but little is understood about their formation. To address this, we irradiated human peripheral blood lymphocytes (PBL) in vitro with 0.5 Gy densely ionising α-particles (mean of 1 α-particle/cell) and analysed the chromosome aberrations produced using 24-colour M-FISH. Our data suggest that complex formation is a consequence of direct nuclear α-particle traversal and show that the likely product of illegitimate repair of damage from a single α-particle is a single complex exchange. From an assessment of the ‘cycle structure’ of each complex exchange we predict α-particle-induced damage to be repaired at specific localised sites, and complexes to be formed as cumulative products of this repair.