The USS Ulysses was a 24th century Federation starship operated by Starfleet. In 2371, the Ulysses was under the command of Captain Entebe.
In that year, the Ulysses conducted a mission to study protoplanetary masses in the Helaspont Nebula.
Shortly after stardate 48962, Captain Sisko suggested contacting the Ulysses to support the USS Defiant respond to a faked distress call from the Federation colony on Barisa Prime.
At the time, the Ulysses was the closest starship in the sector and was twenty hours away, at maximum warp. However, due to sabotage to the communications system by a changeling infiltrator, the Defiant was unable to request assistance. (DS9: "The Adversary")
In the Star Trek Encyclopedia (4th ed., vol. 2, p. 334), the Ulysses was mentioned to be a Nebula-class starship, with the registry NCC-66808.
The Ulysses was named after the Roman word for Odysseus, a hero of the Trojan War in Homer's The Iliad and the main character of Homer's The Odyssey.
The game Star Trek: Deep Space Nine - The Fallen featured a Miranda-class starship with the same name, in service in the 2360s. William Ross served on the ship as first officer. That ship was attacked by the Cardassians and crashed on an uninhabited planet, while investigating an Orb of the Pah-wraith.