MANILA — It would have seemed impossible when Ferdinand Marcos was ousted into exile in Hawaii in 1986 after two decades of largely dictatorial rule, but his son, Bongbong, is poised in advance of elections Monday to return the family name to the presidency of the Philippines. 

Nearly two-thirds of the 110 million Filipinos are expected to vote, and the polls show 64-year-old Bongbong, the nickname by which Ferdinand Marcos Jr. is universally known, is running comfortably ahead of the woman who defeated him for vice president six years ago. 

Bongbong waves and smiles genially at rallies but has avoided debates with his rivals while telling Filipinos their lives were much better when his father ruled from Malacañang, the storied palace that is the center of presidential power. 

Many people one meets are inclined to agree — and either know nothing about or don’t believe the record showing that Ferdinand Sr. and his wife, Imelda, siphoned off about $10 billion into their own coffers before American helicopters lifted them, their family, including Bongbong, and cronies from Malacañang. From there they were flown to Clark Air Base, then an American facility, for the flight aboard U.S. Air Force planes into exile in Hawaii. 

If elected, Mr. Marcos, who was once convicted of tax evasion but never paid up, is expected to get rid of cases that still linger in various courts in hopeless pursuits of the missing billions. His leading foe, Vice President Leni Robredo, 57. promises to clean up corruption, go after favored cronies, and spread the wealth in a society in which poverty is endemic. She easily leads eight other candidates, including the boxer Manny Pacquiao, winner of welterweight, lightweight, featherweight, and flyweight crowns, who’s running well behind despite his fame.

Ms. Obedo evokes thunderous applause at rallies but does not seem likely to break the almost hypnotic appeal of the Marcos name. Mr. Marcos claims repeatedly that the vote count in her vice presidential win six years ago was fraudulent. The national election commission has rejected the claim. 

The outgoing president, Rigoberto Duterte, cannot run for a second term under the constitution adopted after the downfall of Mr. Marcos’s father. The successor of Marcos pere, Corazon Aquino, who led the “People Power revolution” after the assassination in 1983 of her husband, Benigno Aquino Jr., wanted to be sure no one could remain in perpetual power. Corazon Aquino died in 1989. Her own son, Benigno Aquino III, who died last year. was elected to a six-year term in 2010.

Mr. Duterte’s name and family power are certain to live on. His daughter, Sara Duterte-Carpio, mayor of Davao, the Duterte family stronghold on the large southern island of Mindanao, is running for vice president. Often described as Mr. Marcos’s running mate, she’s expected to win in elections in which candidates for vice president run on separate tickets from those for president. 

As for President Duterte, he’s running for a seat in the Senate from which he’s likely to be closely advising Mr. Marcos. Mr. Duterte has been responsible for a prolonged crackdown on drugs in which thousands have died, many without benefit of trial or even arrest. Mr. Marcos, who has served previously as a senator and governor of his father’s native province north of Manila, is not expected to adopt such a tough policy on drugs if only because his advocates say Mr. Duterte has largely solved the problem. 

Mr. Marcos’s campaign for president caps a long-running quest by his family to erase the memory of the corruption and dictatorship for which his father was responsible. Mr. Marcos was 72 when he died in Honolulu in 1989; his widow, Imelda, now 92, battled to have his body returned to the Philippines in 1993, where it remained in deep freeze until he was finally buried in Manila’s National Heroes’ Cemetery in 2016.

Marcos served in the American forces in World War II until his capture by the Japanese. Released more than two years later, he returned  to the American military as it was driving out the Japanese. Medals that he said he received were later revealed as fraudulent.

Voters, professing their love of Bongbong, as well as his father, often say they know nothing about his family’s record of corruption, nepotism, and cronyism. As for what they think of it, they commonly respond, “Prove it,” oblivious of the copious court records and testimony.