An important part of the beam diagnostics of the future superconducting Super-FRS fragment separator at FAIR will be the time-of-flight measurement. The tests of radiation-hard silicon detectors for such measurements at the Super-FRS and the EXPERT project within the Super-FRS Experiment Collaboration are presented. The main part of the current work is devoted to an investigation of the time characteristics of silicon detectors under the irradiation caused by intermediate energy Xe and C beams. The time resolution, obtained for the detector prototypes irradiated with Xe, reaches down to 20 ps, for C ions to 100 ps. These results are presented and discussed.