All the future members of Gemini were still newborn children when the Internation Hospital of Segrate, where they were born, explode due to the outburst of the Meta-Impulse, a semi-demonic-cosmic energy released by the experiment of Edwig Caine, a scientist and ex MI5 agent obsessed with discovering the secret of super-powers.
The Meta-Impulse kills any babies in the hospital, and transform all adults in the area in horribly deformed monsters, including several militar lead by Edwig Caine on the field. The mysterious energy was released while a powerful cosmic/demonic entity, the Nosferath, was involountary freed by it's prison by the experiment of Cain.
The Nosferath and Edwig Cain sealed a bargain, so five infants were resurrected by the demon Nosferath, imbued with a fraction of his powers and given to Caine. Incidentally, the Nosferath also give superpowers to a normal con-artist, trasforming him in it's minion, Mr. Illusion.
It's not clear how the five children spent the following years: maybe, after medical examinations and observation, they were turned back to their family, adopted or raised in governamental structure. The only sure information is that Edwig Caine follow their life and train them. One of them, Gabriel, was rised as his legal son, gaining the surname "Caine". However, thanks to a government coverup, the Italian terrorist organization "Alba Nera" (Black Dawn) was framed as guilty for the explosion.
Years later, the kids, now adult, became the personal anti-terrorist task force of Edwig Caine, called Gemini (since all the 5 children were born the same days, as they was twins, and under the Zodiacal sign of Gemini), even if the first evaluation done by Agent Lancelot for the S.H.I.E.L.D. deny them the autorization to become operative becouse they was too instable and without adeguate training, too ruthless and bloodthirsty.
However, in their first mission against the terrorist organization "Alba Nera", Front [Gabriel] discover the truth about the origin of the Gemini team, the rouse of Edwig Caine and is bargain with the Nosferath, still imprisoned in the basement of Vera Croce ["True Cross", the secret base of the team] and waiting to gain enought power to broke free.
This lead to various events, including the framing of Front for betrayal and killing his father, the disfigurement of Front into a battle with Agent Lancelot, and the alliance with the now homeless Mr. Illusion. Into the final confrontation with the Nosferath and it's minion [Mr. Illusion and Alma Matrix], Gemini [and Lancelot] where nearly defeated and only the intervention of the cosmic entity known as the Voyager [hunting the Nosferath] saved them, banishing the demon in his extradimensional prison and thus freeing the five from his curse but leaving their powers intact. Edwig Caine apparently died on this mission.
After this battle, Carlo Paci, an Italian journalist and only person outside the team having evidence of the truth about the origin of Gemini and the events of the Meta-Impulse, chose to give the heroes a chance, keeping their secret. The same thing do Agent Lancelot, and the Gemini team remain operative in Italy under the watch of S.H.I.E.L.D..
The Official Marvel Handbook Vol. 4, under the entry "Euroforce", report: "Another group with unspecified ties to Euromind is Gemini, an Italian-based team assembled by former British intelligence agent Edwig Caine".
Actually, in the orginal Europa series published by Marvel Italia there is shown no connection between the Gemini Team and Euroforce or Euromind. They are protagonist of two different series, totally separeted, that share only few things: having european heroes, having the same publisher [the now closed Italian Division of Marvel], being published on the same book and only in Italian [and however being both in continuity with Marvel Universe].
Otherwise, official Marvel Database seem to have very few information about the Gemini team, due to the five issue miniserie being writen only Italian