The aging Greek Theo Tomasis, Anthony Quinn, rises from peasant roots to become a mogul who owns oil tankers, airlines, and private Mediterranean islands, and he longs to be elected President of Greece. He is immediately drawn to the considerably younger Liz Cassidy, Jacqueline Bisset, when she visits his island estate with her husband James, James Franciscus, the Senator from Massachusetts. Theo is quickly attracted to her, and, despite the fact that she is happily married, begins to woo her aboard his yacht while James converses with the former Prime Minister of the United Kingdom.
Theo's relationship with his son Nico Tamasis, Edward Albert, is tenuous at best. He pushes Nico to join the family business and to make money in the same way he did. Nico wants to manage his own affairs, and he convinces his father to bankroll his ventures. The plan is to buy older freighters, convert them to oil tankers, and sell them to Saudi oil magnates, allowing oil deliveries to flow outside traditional American corporate controls.
Back in the United States, the Cassidys begin their run for President, eventually winning the primary and the general election. The First Lady, Liz Cassidy, becomes depressed after a miscarriage and bears the weight of public life. Tomasis, who has a surprisingly good relationship with the First Family, offers a vacation on his yacht as a change of pace. The President does not trust Tomasis' shipping business and ties to Arab oil states, so Liz travels alone, much to his anger.
In Greece, the yacht hosts guests and celebrities; Tomasis appears to spend a lot of time with Liz, who is initially restrained. At dinner, Liz joins in a traditional sensual dance with plates being thrown and the others clapping. Liz is drawn to Tomasis' free spirit and joie de vivre and decides to leave the vacation early to return to the United States, much to his protests.
Back in the United States, Liz and James walk along the family beach-front property where the President is assassinated by a sharpshooter. After the funeral, Liz becomes withdrawn again, even as the former President's brother John Cassidy, Robin Clarke (the attorney general), asks her to help promote his campaign. She refuses, and Tomasis privately re-invites her to Greece for a longer stay.
In Greece, the relationship blossoms and Liz's spirits lift. Tomasis' business dealings with Nico become the target of scrutiny by American politicians due to OPEC embargoes and rising oil prices. Freighters are being confiscated, and hundreds of millions in investments are at risk. Upon his return from the United States, Theo asks Liz to marry him. Liz wants to, but worries about appearances; he lays out a fair and financially compelling arrangement that would allow her to leave the Cassidy family fortune behind.
After the wedding, there are growing pains as Lizzie is used to having a voice in her husband's affairs. Theo apologizes for Greek chauvinism, and they learn to navigate each other's cultural differences. The marriage remains loving until Nico dies in an accident, and Theo sinks into depression. Lizzie helps pull him out of his mood, and a lawyer and representative secure a favorable plea deal on the oil manipulation charges. Theo's health declines and a doctor gives him a poor prognosis. He keeps his medical information private as his energy wanes. When Liz wants to shop in Paris, he encourages her to go alone and enjoy herself. She leaves the boat on her vacation, waving, and Theo visits his old peasant home on the coast for the last time, ending with a traditional Greek dance.
