Physically speaking, the delta function like beam-beam nonlinear forces at interaction points act as a sum of delta function nonlinear multipoles. By applying the general theory established by J. Gao (Nucl. Instr. and Meth. A 451 (2000) 545), in this paper we examine analytically the beam-beam interaction limited dynamic apertures and the corresponding beam lifetimes for both the round and the flat beams. Relations between the beam–beam limited beam lifetimes and the beam-beam tune shifts are established, which show clearly why experimentally one has always a maximum beam–beam tune shift, ζy;max, around 0.045 for e+e- circular colliders, and why one can use round beams to double this value approximately. Comparisons with some machine parameters are given.