One of their arch nemeses was Apocalypse.
Apocalypse eventually kidnapped Cyclops' infant son, Nathan Cristopher Summers, and infected him with a virus that could not be treated in the present time. The only way save the child's life was to send him thousands of years into the future, where the technology was available to treat the virus. A clan of women rebels from the future, known as the Askani, sent a representative named Jen to the present time in order to bring Nathan Christopher to the future.
Shortly after this, in 1991, X-Factor and the X-Men teamed up to fight one of the X-Men's oldest foes, the telepathic Shadow King. After the draining battle, X-Factor, who were also Professor Charles Xavier's original X-Men decided to move back to his school/mansion where they had all been taught to control their superhuman abilities.
This left the X-Factor comic book without a team to showcase. Rather than end the successful series, Marvel decided to recreate X-Factor with new members, most of whom were already friends or accquaintance of the X-Men or Professor Xavier.
The new team consisted of Havok, Polaris, Strong Guy, Wolfsbane, Multiple Man, and Quicksilver. The new team functioned under the auspices of the federal government, as a group of mutant "police officers" that The Pentagon could call on to battle other superhuman beings. Dr. Valerie Cooper, a regular human without any abilities, functioned as the liaison between X-Factor and the government and was technically the "leader" of the team.
Shortly, relations between Cooper and Havok, the team's field leader, began to sour, due to suspicions that Cooper had some anti-mutant biases. This hostility culminated when X-Factor discovered that Cooper betrayed them to a corporation that was affiliated with anti-mutant senator, Robert Kelly, and was funding the creation of mutant-hunting robots, called Sentinels.
X-Factor broke ties with Cooper and the mutant X-Man known only as Forge (comics), who has the power of invention, took over as liaison between X-Factor and the U.S. government. Quicksilver, whose marriage to the Inhuman, Crystal, was deteriorating, decided to quit X-Factor and join the Avengers, in hopes of bettering his relationship with Crystal and their young daughter, Luna, both of whom lived in the Avengers' mansion in Manhattan.
Only weeks later, X-Factor was kidnapped by a mutant known as Haven, who wanted to bring about a massive earthquake that would kill off most of the people on earth. While in Haven's custody, Multiple Man escaped and was wondering around, getting sicker and sicker by the moment. It was later revealed that he had the Legacy Virus, and had tried to keep it secret from his team members as long as possible. Haven, who was more misguided than evil, attempted to cure Multiple Man's disease as he was slipping away, but her power only succeeded in killing him — something that she felt horrible about, even though X-Factor believe that she killed him on purpose.
The X-Factor comic book was replaced by Factor-X between February and May of 1995, during a time when all of the X-Men-related comic books took place in an alternate reality, as result of Charles Xavier having been killed in the past, long before ever creating the X-Men. The alternate reality was called the Age of Apocalypse, where, without Xavier and the X-Men's presense, Apocalypse managed to become the supreme ruler of the world, convincing the Beast, Sinister, Havok, and many other mutants to support him. Bishop eventually managed to travel back in time and prevent Charles Xavier's assassination, thus returning the X-Men comics to normal by May 1995.
Later members of X-Factor included former villains such as Mystique and Sabretooth. The comic book ended around 1998 and was replaced with the title Mutant X, in which Havok was thrown into a parallel universe.