Four men lodged separate claims in the Guam Superior Court on Tuesday, three of which accuse Archbishop Anthony Apuron of molesting them when they were children.
Apuron, who denies any wrongdoing, has stepped aside from his duties while he awaits a canonical trial in Rome.
The allegations, which emerged earlier this year, date back to the 1970s when Apuron was a parish priest.
The fourth lawsuit is from another ex-altar boy who alleges he was abused by former priest Louis Brouillard in the 1950s.
All the court cases are seeking unspecified damages from the Church.
"The lawsuits will cause the Church to remove the cancer caused by these paedophile priests and restore the Catholic Church to its rightful glory," said lawyer David Lujan, who is handling all four cases.
Lujan told reporters it would help the plaintiffs by providing "healing of decades-old feelings of fear, embarrassment, shame, hatred and blaming oneself".
Guam's government in September lifted the statute of limitation in relation to sex abuse cases allowing the victims to take their cases to court.
But Lujan said there was no threat to the church's survival on the deeply religious island.
"The lawsuits will not cause the destruction of the church," he said.
"After all, the church has outlived every empire and civil government known to man. The church will reform itself and become even greater."
Archbishop Savio Hon Tai-Fai, who was sent to Guam from Rome to run the Agana archdiocese on an interim basis, said no date had been set for Apuron's trial.
He confirmed the Vatican had nominated a US cleric, bishop Michael Byrnes, to take over his duties at the end of the month.
Byrnes, from Detroit, is technically a "coadjutor archbishop", meaning he serves alongside Apuron, although Hon said he may take over in the long term.
"Coadjutors have successions rights when bishops resign retire or are removed. This appointment suggests a more permanent solution," he told reporters.
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