When Venezuela President Hugo Chávez announced that his cancer was back and he was returning to Cuba for surgery, he was flanked by two men: On his left was his vice president, Nicolas Maduro, and on his right was Diosdado Cabello, president of the National Assembly. The presence of these two men is significant.

Chávez was sending an unambiguous message to his supporters. If his health were to prevent him from finishing out his term — or being sworn in Jan. 10 for his fourth term, as the information minister has said might be a possibility — these were men he trusted to continue his “Bolivarian Revolution.”

The United States will carefully watch how these developments unfold over the next months.

Relations between the United States and Venezuela have ranged from difficult to hostile since Chávez took office in 1999 and began to implement what he calls “21st century socialism.” I was U.S. ambassador to Venezuela from early 2002 till late 2004 as relations went from bad to worse. Chávez blamed a failed 2002 coup against him on the United States (not true), nationalized U.S. companies, insulted the president of the United States and blamed “the empire” — his term for the United States — for every ill.

In 2008, Venezuela expelled the U.S. ambassador for nearly a year, and since 2010, neither country has permitted the other to post an ambassador in its capital.

Chávez polarized Venezuelan politics and gained complete control of all five branches of government — yes, the 1999 Constitution establishes five branches of government. In foreign affairs, the government actively supports the Assad regime in Syria, rejects sanctions on Iran and generally opposes the U.S. at every turn.

Throughout his presidency, the U.S. has continued to be Venezuela’s most important trading partner. Although net U.S. imports of Venezuelan oil are at a 30-year low, it is our fourth-largest supplier of imported oil, and we buy nearly half of Venezuela’s oil exports.

Despite its oil riches, Venezuela is deeply in debt. Government spending increased by 40 percent in 2012. Expect the next president to devalue the bolivar to curb inflation, now running at 18 percent.

What are the chances that either of the potential candidates can keep chavismo alive without Chávez?

In October 2003, I walked out of a lunch into a gaggle of reporters shouting, “Is the head of the CIA in Venezuela?” It seems that Maduro, then the National Assembly deputy, and two colleagues had told a news conference that they had a video showing the “CIA’s head of Latin American operations” getting off a plane in one of the country’s state capitals. While they did have a video of an American in a suit getting off a private plane, the gentleman was the human resources director of a U.S. company considering an investment in Venezuela.

These wild accusations say much about Maduro, who calls himself the political “son” of Hugo Chávez. Maduro is viscerally anti-American, opposes the checks and balances of liberal democracy and distrusts free markets.

The unknown factor is whether Chávez can transfer his popularity to Maduro with a point of his finger, a dedazo. No one has ever accused Maduro of being charismatic.

As for the man who was on Chávez’s right, Cabello has two bases of support: Chávez and the military. The military high command is filled with Cabello’s cronies. If there are elections, Henrique Capriles, who won relection Dec. 18 as governor of Miranda state, will be the opposition candidate. He did an extraordinary job in October campaigning for the presidency on a platform of open markets plus social programs for the poor. For once, the pundits are prudently refraining from predictions. There are simply too many moving pieces. Pick your favorite scenario: An ailing Chávez remains in office, a victory by Maduro or Cabello, a battle between Maduro and Cabello, or an opposition victory.

My bet is that a deeply polarized and de-institutionalized Venezuela will be both turbulent and unstable for the foreseeable future.

Charles Shapiro is president of the Institute of the Americas, a public policy think tank at UC San Diego. He was the U.S. ambassador to Venezuela from 2002 to 2004.