The New MutantsMarvel Comics universe.
They originally started by Charlie Xavier when he was under the control of a member of a menacing alien race called The Brood. The young ones were intended to be hosts for the race for reproduction. However, the team soon learned of the alien and defeated it, although they were unaware of Xavier's condition. Eventually, the X-Men, which Xavier claimed were dead, but were actually in space fighting the species with the help of the Starjammers, returned to save Xavier and in the process momentarily fought the kids. That encounter was interrupted when Xavier reappeared and transformed into a Brood Queen which was eventually subdued and Xavier's consciousness was given a new cloned body. Xavier decided to keep the young students, deciding that a class for younger mutants who were not intended to participate in the X-Men's missions was appropriate despite the team's origin.
The line up included Cannonball, Karma, Magma, Wolfsbane, Sunspot, Cypher, Psyche, Warlock and Magik. Later when the X-Terminators disbanded Boom-boom and Rictor joined and it was at about this time that the new mutants decided they no longer wanted to be "X-men juniors".
However, working outside the X-men family didn't go well and the team mainly got into trouble, that was until Cable took over as team leader. Most of the New Mutants quit (except Boom-boom and Cannonball). But when Cable changed the team name to X-Force a whole new team was put together (nb. later Sunspot and Rictor rejoined X-Force).