His sister-in-law, Therese Hunkin, didn't disclose the cause of death but said he died at his home in Provo, Utah.
"He passed away peacefully at his home surrounded by family and a few close friends," Hunkin said in a brief phone interview from Provo late yesterday.
The House delegate for American Samoa, which is a US territory about 2,300 miles south of Hawaii, can vote in committee but not on the House floor.
Faleomavaega, a Democrat, became a congressional delegate in 1989.
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He "had served the people and government of American Samoa faithfully for many years," said American Samoa's acting governor Lemanu Palepoi Peleti Mauga.
Faleomavaega began his Washington career in 1973 as an administrative assistant to Paramount Chief A.U. Fuimaono, the territory's first elected representative to Washington. He then served as staff counsel to the House Committee on Interior and Insular Affairs from 1975-1981 before returning to American Samoa as its deputy attorney general.
"It is with pleasure that I say that life with Eni was far from dull," his wife, Hinanui Hunkin, told The Associated Press via email from Provo on Wednesday night. "I am so grateful for the trust that the people of American Samoa, for so many years, placed in him as their servant. I love and miss you, American Samoa."
Born in American Samoa, Faleomavaega graduated from Kahuku High School in Hawaii in 1962. He then earned a bachelor of arts in political science and history from Brigham Young University in Utah in 1966.
Faleomavaega served in the House for 25 years before he was unseated in 2014 by Republican Aumua Amata Radewagen. He is survived by his wife, five children and 10 grandchildren.