The double ionization of argon and xenon in an intense laser field has been studied in detail using an electron-ion coincidence technique. The observed double ionization electron spectra in xenon show resonancelike structures here resolved for the first time. In argon, the featureless spectra are consistent with rescattering. This represents a clear transition in the dynamics of strong-field double ionization, analogous to the well-known transition between the tunneling and multiphoton regimes in single ionization.