Regularity and chaos of “quasi-stable” (i.e. appearing stable during a finite interval of time) planetary orbits around one component of binary stars is investigated for different values of the binary's mass ratio and orbital eccentricity $e$. The behavior of fictitious planetary orbits around 16 Cyg B-like stars is presented. Among the quasi-stable orbits we found that there exists a (“stability zone”) for every values of $e$, but that the existence of nearly-circular planetary orbits is restricted to values of $e$ less than 0.8. However, not all the quasi-stable orbits are regular: emergence of chaos when $e$ increases is shown in two sets of quasi-stable orbits (each set has fixed initial conditions for the planet, but varying values for $e$ from 0 to 0.99). In the first set, which lies in the “heart” of the stability zone, chaos appears only when $e$ approaches 1. The second one is near the border of the stability zone, and chaos appears as soon as $e$ reaches 0.7. The influence of the binary's orbital eccentricity on the limit between regularity and chaos is therefore stronger in the latter case (wider planetary orbits) than for the former one (closer planetary orbits).To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html