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Team X is the mutant task force at the centre of Marvel's Wolverine. Nathaniel Essex formed it to help protect mutants in a world where they live hidden and hunted, and Insomniac has described it as a black-ops group fighting for mutant survival, taking its inspiration from the comics team of the same name without adapting a specific story.
Logan's return

Logan walked out on the team three years before the game begins, and the campaign opens with him rejoining it. That gap is the source of most of the group's internal tension, and it is deliberately unexplained at the start.
The first mission is a rescue. Insomniac's own wording is that Logan rejoins his former team for a critical mission to infiltrate Trask's outpost and save Nathaniel Essex, and that this sets the stage for the story. It plays out in the wilds of Telambang, where Logan fights through Reaver forces, Hand ninjas and a run-in with Omega Red to reach him. See Story and Setting.
Confirmed members

Member | Notes |
|---|---|
The player character. Rejoins the team after a three-year absence. | |
Shifts through identities as a fight demands. Commandable in at least one boss encounter. | |
Referred to as Victor in dialogue. Antagonises Logan throughout the opening. |
That leaves three confirmed members. Sabretooth and Mystique are now named outright as Team X members in official material, which is firmer than the earlier wording that only had them operating under Essex. No further members have been named. Two separate accounts have each proposed a different fourth member, neither of them from Insomniac and neither corroborating the other, so this page does not list one.
Nathaniel Essex sits outside that count. Insomniac's wording is that he formed the team; it has not called him a member or its leader, and coverage that does is going beyond what the game has shown. When the game opens he is Trask's captive, which makes him the first mission's rescue target rather than someone fighting alongside Logan.
Internal tension
The group is not a comfortable one. Sabretooth feels spurned by Logan's original exit and spends the opening needling him, calling him runt and at one point body-slamming him at the Princess Bar in Madripoor. Previews describe the two constantly butting heads.
The team also has quieter moments. After the first act the Princess Bar becomes a walkable space where Logan talks to the people around him, including the Never Have I Ever scene with Mystique. See Locations.

Fighting as a team
Allies are part of the combat system rather than background characters. Logan can call one in mid-fight, Critical Strikes can be performed jointly with another character, and in the Sentinel Prototype encounter Mystique can be ordered to take a sniper shot. Marcus Smith has described Sabretooth's help, less flatteringly, as being like stealing your kills.
The game is not co-op and there is no character switching, so allies are always a tool the player directs. Trask's Ability Inhibitors block the whole team's abilities at once, not just Logan's, which is what turns those fights into a rush to destroy the hardware. The Sentinel Prototype in particular is described as requiring the combined abilities of Team X to bring down.
One team move has been described first hand. During the Sentinel Prototype fight Logan can be thrown at a target by Sabretooth rather than closing the distance himself, which is the closest thing the game has shown to a signature pair manoeuvre. See Enemies and Factions.
Jean Grey
Jean Grey is a new ally rather than a team member. She is protecting a group of captured mutant teens on her own, and she and Logan fight together and can perform takedowns as a pair, but nothing in official material places her inside Team X. See Characters.
The Essex Institute
A location named after the man who formed the team has been described as a hub Logan moves through between missions, likened to a school for gifted mutants. It rests on a single account, Insomniac has not detailed it, and it is not clear whether Team X operates out of it or merely passes through. Treat it as provisional until official material says more.