In 2374, they were on the verge of war with the Vaskans. The Vaskans, who saw the Kyrians as a violent, stubborn people, claimed to have have tried every diplomatic option, but expected an attack any day. The trigger for the war appeared to be when USS Voyager signed a trade agreement with the Vaskans, which a Kyrian leader called Tedran interpreted as them negotiating an alliance to attack the Kyrians.
Voyager was attacked by three Kyrian ships, and a group of Kyrians led by Tedran beamed aboard Voyager and took several people hostage and collected technology. They were defeated by Voyager security personel, but at the eve of surrender Tedran was killed by the Vaskan ambassador, Daleth. After this, Voyager was attacked by nine more Kyrian ships. It was speculated that the EMH backup module was stolen during this battle.
Voyager was believed to have then left the area sometime later. The Great War ensued, which was later described as brief but brutal.
By the 31st century, a Kyrian struggle for equality was ongoing. Kyrians were forced to live outside of city centers, and their children could not attend the same academies as those of Vaskans. Token Kyrians might be included in commissions.
During this period, a man named Quarren founded the Museum of Kyrian Heritage. Among its exhibits was one called The Voyager Encounter. However, after seven centuries the Kyrian view of the event was severely distorted. They believed that Voyager was a warship that had been hired by the Vaskans to attack Kyrian lands and that the Vaskans promised them the location of a wormhole in exchange. In their version of events, Voyager's doctor created biogenic weapons responsible for eight million deaths, and Janeway coolly executed Tedran, who was by now regarded as a Kyrian martyr.
This version of events was upended by the discovery of a back-up copy of The Doctor in an EMH backup module found beneath the ruins of Kesef. After being sent to the Museum of Kyrian Heritage, Quarren managed to reactivate this version of the Doctor, initially considering him a war criminal. However, the Doctor protested the revisionist history, and eventually started to win over Quarren and the rest of the planet. Within years, the two species witnessed the dawn of harmony. (VOY: "Living Witness")