A total of 23500 Extensive Air Showers (EAS) with energies above ˜10^16 eV have been detected during the ˜3500 hours ofthe Horizon-T (HT) detectors system operations before Aug. 2016. Amongthese EAS, more than a thousand had an unusual spatial and temporarystructure that showed pulses with several maxima (modals or modes) fromseveral detection points of the HT at the same time. These modes areseparated in time from each other starting from tens to thousands of ns.These EAS have been called multi-modal. Analysis shows that themulti-modal EAS that have been detected by Horizon-T have the followingproperties: 1. Multi-modal EAS have energy above ˜10^17eV. 2. Pulses with several modes are located at large distances from theEAS axis. An overview of the collected data will be provided. Generalcomments about the unusual structure of the multi-modal EAS will bepresented.