[en] We present experimental studies of the photodetachment process in negative ions subjected to a strong laser field. A negative ion represents an atomic system where the outer electron is bound to the atomic core by a short-range potential. Therefore, negative ions are best suited to verify predictions of Keldysh-like theories, where the electron interaction with the core is neglected in the description of the final continuum state. In our experiments we measure the angle resolved momentum distributions of the photoelectrons ejected from negative ions in laser fields with a peak intensity reaching 5 x 10¹⁴ W/cm². Under such strong field conditions the electron yield at high kinetic energies is found to be due to the process of sequential double detachment. In the present work we investigate this process for different ions having various ratio of electron affinity to ionization potential. In particular, experiments are performed on Br^-, F^- and H^-. The measured spectra are compared with the predictions of the strong field approximation. The effect of core polarization in the sequential photodetachment is discussed