Among the 48 known multiplanetary systems, some are in mean-motion resonances (in most cases in the 2:1 mean-motion resonance). Although until now no extrasolar planetary systems have been found in a 1:1 mean-motion resonance, many studies are dealing with this configuration. Besides the well-known motion of the Trojan asteroids, further possibilities exist for stable configurations of planets or satellites in a 1:1 resonance. For one thing, we can find so-called exchange orbits in our Solar system (Janus and Epimetheus), where both Saturnian moons exchange the values of their semi-major axes (exchange-a configuration) when approaching each other. In addition, we can also find similar behaviour for two planets on orbits with the same semi-major axis, but with different eccentricities; here an exchange of eccentricities takes place (exchange-e configuration). In this work we focused on the second possibility and performed a parameter study by varying the initial conditions (mass and eccentricity) of two planets on exchange-e orbits. By means of an extensive numerical study, we can find a wide variety of initial conditions leading to long-term stable orbits.