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After their weekend wedding in the Mediterranean principality, they arrived on Tuesday in Durban, where Charlene used to train for South Africa's Olympic swim team.
The trip is part honeymoon, part business.
Albert is a member of the International Olympic Committee, which is meeting in Durban to vote on Wednesday on the venue for the 2018 Winter Games.
Zuma greeted them on Tuesday at the official opening of the session, where Charlene's appearance in a black gown was splashed across South African media.
Lobola
The polygamist president, who has four current wives, teased Albert about adhering to South Africa's tradition of grooms giving cattle to the bride's family, a gift known as lobola.
"She has again done us proud by bringing us the royal in-laws from Monaco," Zuma said in welcoming Charlene.
"We usually say you can't get a wife free of charge, you must pay lobola - the cattle," Zuma joked.
Zuma invited the couple to lunch with him on Wednesday at King's House, the presidential residence in Durban, a stately cream-coloured building with columns and balconies overlooking the sea and Moses Mabhida Stadium.
Fine, how are you?
The couple arrived all smiles for the assembled press, with Charlene in a white crochet dress, greeting reporters' questions with a simple "Fine, how are you?"
They shook hands with Zuma and his third wife Thobeka Madiba Zuma, smiled for the cameras and went inside for a late lunch.
Once the official Olympics business is finished, the couple are throwing a reception on Thursday for 400 guests at the five-star Oyster Box hotel in the resort town of Umhlanga, just north of Durban.
The town has draped its streetposts with the flags of Monaco and South Africa.
Gushing guests
Guests at the hotel have gushed to South African media about their chance encounters with Charlene.
"My golly, it had been only about 20 seconds after walking out that I saw this lovely tall person, from the rear. She then turned around and I saw it was Charlene," 90-year-old Mavis Warder-Griffin told The Star newspaper.
"She said hello and put her hand out to shake mine. It was really unbelievable, all a lovely, lovely surprise. What a delightful person. It was one of those unexpected events, and I am on cloud nine. I don't think I'll wash my hands, I've touched royalty."
Her daughter Meryl Marshall was also enthralled, saying: "Her beauty took my breath away. She was warm and friendly and will be a wonderful ambassador for South Africa."
Charlene's warm reception home has largely overshadowed reports of rumours that she had tried to flee to South Africa before the wedding, with newspapers instead running stories about "our royal couple".
Palace officials in Monaco said there had been a "hiccup" in the wedding preparations when Charlene learned that Albert may face demands for a paternity test after a claim by a former lover.
