The Exoi Kritocracy's military consisted of an army and navy, led by a War Judge, with the Governing Judges as the commanders-in-chief.
The navy was used primarily for transport purposes, but its capital ships were heavily armed and armored for ship-to-ship combat as well. All Kritocracy vessels had numerous lasers and turbolasers, but the navy had relatively few starfighter analogues. Unlike the ground forces, many naval divisions had a number of alien crewers.
The pride of the Exoi war machine was its ground force. The Exoi had two primary ground assault components: war droids and Exoi battle armor. War droids came in many varieties, ranging from humanoid and Exoid robots to mobile weapons platforms and walking tanks. Exoi battle armor was usually fitted to the Exoi pilot, and thus ranged from roughly 2.5-3.0 meters tall; more exotic variations could seat multiple pilots. The Exoi sometimes used non-Exoi as ground auxiliaries.
Kritocracy strategy usually relied on overwhelming targets in space by sheer number of capital ships and weapons emplacements, then deploying the army to the ground. War droids were often used for large-scale destruction, especially in their early generations when they could not easily be programmed to discriminate in the application of force. Exoi in battle armor tended to take the lead when targets needed to be taken relatively intact; Exoi battle armor pilots also sometimes commanded war droid units.
The Kritocracy often adapted to new threats over time, and various generations of battle armor had seven legs (like the Exoi themselves), two legs, four legs, or even treads, as well as a wide arsenal of weapons depending on their targets. Despite its centuries of successes and continually evolving weapons, the Kritocracy was defeated by the Chiss Ascendancy in the Kritocracy-Ascendancy War when the Chiss exploited the Kritocracy's lack of starfighters, using their own fighter craft to carve up Kritocracy carriers and battleships before they could disgorge their cargo of war droids and Exoi battle armor pilots.
After losing the war, the Kritocracy began four millennia of atrophy and decay, hemorrhaging hundreds of systems initially, then slowly losing more to rebellion, economic catastrophe, and occasionally even abandonment. When it was not actively putting down rebellions, the military functioned mostly as a backup police force, and lost a great deal of public respect. As more systems slipped through the Kritocracy's fingers and resources were unavailable to repair or replace the fleet and the ground forces, many war droids and suits of battle armor decayed and become nonfunctional. By the time the Kritocracy finally folded and its worlds joined the Golden Empire in 155 ABY, only the capital world of Toriafas was well-defended, and Queen Rin Sakaros and Prime Legate Sorrik both felt the Prime Fleet could take the planet by force if necessary.