We study the effect of cavity topology on the nonlinear dynamics of additive-pulse mode-locked (APM) lasers configured in the Fabry-Perot and Michelson geometries. In experiments the Fabry-Perot laser often exhibits such behaviors as period doubling and quasiperiodicity as the nonlinearity is increased, whereas the Michelson APM (M-APM) exhibits none of these effects. Numerical studies confirm that the M-APM appears to be more resistant to such behavior and thus is more tolerant to excessive nonlinearity in the control cavity. Using the concepts of intensity- and phase-dependent two-beam and multiple-beam interference, we obtain a general empirical rule connecting cavity topology to pulse train instabilities for fast saturable absorber mode-locked lasers employing coupled cavities. (C) 1998 Optical Society of America. [S0740-3224(98)01910-9]. OCIS codes: 140.1540, 140.4050, 140.1700, 320.7090, 320.7110.