A microemulsion of decane droplets stabilized by a nonionic surfactant film is progressively charged by substitution of a nonionic surfactant molecule by a cationic surfactant. We check that the microemulsion droplets remain identical within the explored range of volume fraction (0.02-0.18) and of the number of charges per droplet (0-40). We probe the dynamics of these microemulsions by dynamic light scattering. Despite the similar structures of the uncharged and charged microemulsions, the dynamics are very different. In the neutral microemulsion, the fluctuations of polarization relax, as is well-known, via the collective diffusion of the droplets. In the charged microemulsions, two modes of relaxation are observed. The fast one is ascribed classically to the collective diffusion of the charged droplets coupled to the diffusion of the counterions. The slow one has, to our knowledge, not been observed previously neither in similar microemulsions nor in charged spherical colloids. We show that the slow mode is also diffusive and suggest that its possible origin is the relaxation of local charge fluctuations via the local exchange of droplets bearing different numbers of charges. The diffusion coefficient associated with this mode is then the self-diffusion coefficient of the droplets.