The components, working principle and characteristics of FATIMA (FAst TIMing Array), a fast-timing detector system for DESPEC at FAIR, are described. The core system includes 36 LaBr 3 (Ce) scintillator detectors, a mounting frame for the DESPEC station and a VME-based fast-timing data acquisition system. The current electronic timing circuit is based on V812 constant fraction discriminators and V1290 time-to-digital converters. Gamma-ray energies are measured using V1751 digitisers. Characteristics of the core FATIMA system including efficiency, energy, and coincidence resolving time, as well as limitations, are discussed on the basis of test measurements performed in the S4 cave at GSI, Germany. The coincidence -time resolution for the prompt 60 Co cascade is determined to be ∼320 ps full width at half maximum. The total full energy peak efficiency at 1 MeV for the 36 detector array in the DESPEC setup is 2.9%. The energy-dependent prompt response centroid curve with the current CFD/TDC combination is shown to be smooth; the centroid shift method can be applied for the measurement of half-lives below 200 ps. An overview of applications of the FATIMA detectors as an ancilliary system in combination with other detector arrays during recent years is given. Data on the operation of the detectors in the presence of magnetic fields are presented.