By Terry Wade and Patricia Velez

LIMA (Reuters) - Humble crowds adore her populist gestures. Fans and critics alike call her the co-president. Her husband, a rebellious army officer turned moderate leader, says people who think his wife is too influential are sexist.

Peru's first lady, Nadine Heredia, is a potent political force. A telegenic 36-year-old mother of three who started the Nationalist Party along with President Ollanta Humala, she weighs in on a range of policy issues behind the scenes and, in public, often serves as the government's messenger.

Her prominent role has made her more popular than Humala - so popular that she is widely viewed as a potential successor to the 50-year-old president.

She is arguably her party's only viable candidate after Humala and could become Peru's first female president if an anti-nepotism law is struck down to allow her to run in 2016.

Though Heredia insists she has no such plans, she has a remarkable knack for headlining events that feel like campaign rallies, often touching on her parents' roots in Ayacucho, a poor province in the Andes.

"Many of you might be migrants who have come to the capital looking for opportunities," she recently told cheering fans in Puente Piedra, a hardscrabble neighborhood on the outskirts of Lima where she led a workshop on preventing dengue fever. "We have to help each other because I'm the daughter of migrants and know the obstacles one has to overcome!"

After the speech, Heredia was whisked away in a dinky motorcycle taxi, one of the three-wheeled put-puts common in the developing world. It was festooned with balloons.

Minutes later, bodyguards ushered her into her real ride: an imposing SUV.

Heredia is as comfortable on the streets as she is posing for the covers of society magazines in designer gowns.

Her approval rating of 60 percent is 7 points higher than her husband's, Ipsos says. That is remarkable because Humala's twinning of pro-investment economic policies with expanded social welfare programs has made him Peru's most popular leader in years.

Still, his often reserved nature - he did not speak in public for the first two weeks of his term - has made him reliant on his outgoing wife. When Humala first entered politics he tried to improve his wooden speaking style by studying recordings of himself, according to a founder of his party.

Humala has since begrudgingly embraced public speaking but lacks the inspired zeal of his predecessor, the grandiloquent Alan Garcia. Humala often mumbles or mixes concepts by speaking off the top of his head.

Political veterans say Heredia elevates his game.

"Peru would be far worse off without Nadine," said a former cabinet official under Garcia. "Humala is aware of his limitations. That is why he depends on her."

Most of the dozen people interviewed for this article, from lawmakers and political operators to former cabinet officials and voters, referred to Heredia as "La Presidenta."

Sometimes they were joking. Other times, it was inadvertent. But they all said Heredia is Humala's most important adviser.

When people ask if she will be a candidate, Heredia relies on a pair of stock phrases: "I'm not thinking about this now," or "This isn't in my plans."

Neither amounts to a categorical denial. Aides said Heredia was not taking political questions at this time, but they emphasized that she ignores polls and that her role is to support her husband by "walking alongside him - neither in front nor behind him."

POWERFUL ADMIRERS

Heredia has won the respect of other powerful women in the Americas - including two former first ladies.

At a women's development forum in Lima in October, former U.S. Secretary of State Hillary Clinton - thought to be considering a run for president in 2016 - was keen to spend time with Heredia, whose story resonates with her own, according to a former U.S. State Department official.

"She (Heredia) is widely seen as very smart and a key adviser with political ambitions to succeed her husband. So the Hillary Clinton-Nadine Heredia meeting was a natural, beyond just protocol," the former official said.

Argentine President Cristina Fernandez has spoken in glowing terms about Heredia.

"I made a complaint to President Humala that I must mention. When I saw him walking alone I asked 'Where's Nadine?'" she said during Humala's visit to Buenos Aires in November.

"She's a charming woman and a true political force," said Fernandez, who succeeded her late husband, Nestor Kirchner, as president.

Heredia's international profile is set to grow. This week she formally takes on a global role as a U.N. Special Ambassador for nutrition. The post is largely ceremonial, but will give her a platform to hold formal meetings with foreign officials.

PROMINENT ROLE

Heredia was active in politics as far back as her days at the University of Lima, where she studied communications.

Humala's mother is Heredia's cousin and he reportedly first met her when he went to see her father about an accounting question. They married in 1999.

The following year, Humala led a brief military revolt to demand former President Alberto Fujimori step down. Fujimori's government was already falling apart because of scandals but the gambit catapulted Humala to fame as a defiant outsider.

Humala and Heredia founded the Nationalist Party in 2005 and in 2006 Humala launched his first bid for the presidency. He ran as a hardline leftist and narrowly lost.

In 2010, when Humala was moderating his views and trying to address concerns about his radical past, a pregnant Heredia was by his side at a lunch with Wall Street analysts at J.P. Morgan in New York, said an investor who was at the meeting.

Heredia was by all accounts central to the decision to pick economist Luis Miguel Castilla to be finance minister, a move that calmed markets when Humala was elected in June 2011.

"The government has pleasantly surprised the business community," said Humberto Speziani, the head of Confiep, Peru's business chamber. "I had the privilege of knowing Humala and Nadine before they were presidents," he said in a slip of the tongue that reflects a wider view that they govern together.

Heredia was also the first person in the government to publicly urge Humala to oust one of his two vice presidents over a corruption flap shortly after taking office. She did so via twitter.

She has made comments that implied to some people that she thinks she outranks members of the cabinet. "Where's my minister?" she demanded at an event last year while looking for Education Minister Patricia Salas, who reports to Humala.

Critics said the gaffe revealed a bossy side rarely seen in public, where Heredia smiles broadly for minutes on end.

Over the years, Heredia has deflected periodic attempts by opponents to link her financially to fiery Venezuelan President Hugo Chavez. Critics allege she worked for a private Peruvian organization that promoted national "identity and development" and a Venezuelan newspaper that had ties to allies of Chavez. She has called the allegations baseless.

Former allies say she can play political hardball.

Javier Diez Canseco, a left-wing lawmaker who quit Humala's party last year saying the president had swung to the right, said Heredia played a role in getting him suspended from Congress for three months over an alleged conflict of interest.

"I know of people who received phone calls in the name of the first lady or directly from her to vote a certain way."

Her aides had no comment on the allegation.

Heredia is so influential that people often ask her via twitter (@NadineHeredia) to define the government's official line on the main issues of the day. That is partly because Humala sometimes stays silent on divisive issues. She generally avoids responding to the pleas.

Humala's mercurial father has called his daughter-in-law "drunk on power" but the president says people who think his wife has too large a role are stuck in the past.

"It is unfortunate that certain sectors of the political class are male chauvinists who only want to see women relegated to subordinate, domestic roles," Humala has said.

PATH TO OFFICE

While Peru's constitution prohibits Humala from running for a second straight term, the rules on whether Heredia can be a candidate are muddled.

A so-called lower level law, which Humala has criticized, bans members of the president's family from succeeding him.

But the head of Peru's national elections court and a justice on the constitutional court have both said the law should be thrown out because the constitution guarantees any Peruvian the right to run for the presidency.

There are two ways the law could be overturned: by a court once a lawsuit is formally filed, or by Congress.

Political analysts say it may be better for Heredia to wait until 2021 to run. Then she could avoid any talk of nepotism and pitch herself as a wiser candidate in her mid-40s.

But if she does run in 2016, she could pitch herself as someone experienced in governing and might benefit from the public support for Humala's many public works projects.

One potential rival, former lawmaker Keiko Fujimori, whose jailed father was president and who lost to Humala in the 2011 race, has opposed any rule changes for the next election.

Alan Garcia, 63, who is expected to run for a third term in 2016 and is a formidable campaigner, has welcomed a bid by Heredia. His APRA party believes Garcia could trounce Heredia, in part because in a run-off against her he would likely pick up votes from Fujimori's right-wing party.

"I think it is a good idea," Garcia has said of a Heredia candidacy. "It would refresh the political scene. She is a young person who is politically restless."

(Additional reporting by Marco Aquino in Lima and Brian Winter in Sao Paulo; Editing by Kieran Murray and Claudia Parsons)