Two mutually coupled chaotic diode lasers exhibit stable isochronal synchronization in the presence of self feedback. When the mutual communication between the lasers is discontinued by a shutter and the two uncoupled lasers are subject to self-feedback only, the desynchronization time is found to scale as A d τ where A d > 1 and τ corresponds to the optical distance between the lasers. Prior to synchronization, when the two lasers are uncorrelated and the shutter between them is opened, the synchronization time is found to be much shorter, though still proportional to τ . As a consequence of these results, the synchronization is not significantly altered if the shutter is opend/closed faster than the desynchronization time. Experiments in which the coupling between two chaotic-synchronized diode lasers is modulated with an electro-optic shutter are found to be consistent with the results of numerical simulations.PACS numbers: 05.45. Vx, 42.65.Sf, 42.55.Px Chaotic systems are characterized by an irregular motion which is sensitive to initial conditions and tiny perturbations. Nevertheless, two chaotic systems can synchronize their irregular motion when they are coupled [1]. When the coupling is switched off, any tiny perturbation drives the two trajectories apart. The separation is exponentially fast, and it is described by the largest Lyapunov exponents of a single system.In this Letter we show that the trajectory dynamics of coupled chaotic systems which also poses time-delayed self-feedback, is different. In a system with self-feedback, which has also been investigated in the context of secure communication with chaotic lasers [2], the time scale for the separation of the trajectories is found to be much longer than the coupling time. On the other hand, when the coupling is switched on, resynchronization occurs on a faster time scale. We investigate this phenomenon numerically and show first experiments which support our numerical simulations. The demonstrated difference between de-and re-synchronization can be used to improve the security of public-channel communication with chaotic lasers [2].Semiconductor (diode) lasers subjected to delayed optical feedback are known to displays chaotic oscillations. Two coupled semiconductor lasers exhibit chaos synchronization. Different coupling setups such as unidirectional or mutual coupling and variations of the strength of the self and coupling feedback result in different synchronization states: the two lasers can synchronize in a leaderlaggard or anticipated mode [3,4], as well as in two different synchronization states; achronal synchronization in which the lasers assume a fluctuating leading role, or isochronal synchronization where there is no time delay between the two lasers' chaotic signals [2,5,6,7,8].In this Letter we focus on a symmetric setup, the time delay between the lasers is denoted by τ c and the time delay of the self-feedback is denoted by τ d . In the event of τ c = τ d = τ and for a wide range of the mutual coupling strength, σ, and the stre...