Two fast interaction trigger systems based on fast detectors with MCP-PMTs and SiPMs readout have been developed for fixed target experiment Baryonic Matter at Nuclotron and collider experiment Multi-Purpose Detector at Laboratory of High Energy Physics, Joint Institute for Nuclear Research. These detectors provide the effective L0 trigger for nucleus–nucleus collisions and the start pulse T0 for TOF detectors with picosecond time resolution. Important requirement to the detectors is good operation in a strong magnetic field. •L0 trigger systems for heavy ion experiments at JINR are described.•The MCP-PMTs and SiPMs are used for readout in Cherenkov and scintillation detectors.•The detectors operate in a strong magnetic field.•T0 pulse with picosecond time resolution is produced for TOF detectors.