Ann Louise Bardach, The New York Times

THE tribute concert Aug. 12 for Fidel Castro’s 85th birthday, at the Karl Marx Theater in Havana, was billed as the Serenata de la Fidelidad (the Serenade to Fidelity). In terms of flat-footed plays on the name of Cuba’s maximum leader, I prefer “The Fideliad” — which speaks to his epic, exhausting and endless run, which began in 1959.

Some 5,000 concertgoers turned out for the homage by 22 singers, including Omara Portuondo of the Buena Vista Social Club, but the guest of honor was not present. Instead, he settled for a quiet celebration with family, his 80-year-old brother and presidential successor, Raúl, and his devoted disciple, President Hugo Chávez of Venezuela. The irrepressible Mr. Chávez broke the news on Twitter late Saturday: “Here with Fidel, celebrating his 85th birthday! Viva Fidel!”

Over the last decade, the two leaders have celebrated quite a few birthdays together. For his 75th in 2001, Mr. Castro trooped to Caracas for a bash with Mr. Chávez, who hosted a Champagne gala, followed by a nautical tour of Venezuela’s rainforests. The visit, Mr. Chávez said, “gives us an opportunity to let him know how much we love him.”

It’s unclear how many birthdays are left for either leader. Both are now facing their greatest challenges yet, not from opposition movements or dissidents, but from their own failing bodies. Mr. Castro nearly died in 2006 during a botched colon surgery to treat a pernicious case of chronic diverticulitis. He passed his 80th birthday lying in a hospital bed, connected to an antibiotic and nutrient drip. Sitting beside him was Hugo Chávez, who has been there at every stage of Mr. Castro’s five-year convalescence, casually jetting into Havana as if it were a stroll around the block.

Now the 57-year-old Venezuelan is fighting for his own life, after a baseball-size tumor was removed from his abdomen in Havana’s top hospital in June. It was Fidel Castro, not an oncologist, surgeon or family member, who delivered the bad news to Mr. Chávez post-surgery, and who outlined his prognosis and treatment — along with his usual tips on public relations and political strategies. It is likely, based on his surgeries, symptoms and treatment, that Mr. Chávez has metastasized colorectal cancer. After surgery and radiation, he is probably undergoing at least six months of chemotherapy, again in Havana, where he just finished his second round.

As it turned out, Mr. Castro spent much of his birthday giving his friend a pep talk. “We spoke about everything,” Mr. Chávez related upon his return to Caracas. “He said to me: Chávez, ‘You yourself can begin to convince yourself that everything’s over. ... No, no, it’s not over.’ ”

Ironically, the hemisphere’s most indomitable strongmen and determined foes of the United States and free market economics have both been felled, at least for now, by abdominal woes — their guts, as it were. It’s just one more anomaly shared by the leader of the country with the world’s largest reserve of oil and that of a debt-saddled island in the Caribbean.

The symbiosis between Cuba’s emeritus or former (and in most ways, still de facto) commander in chief and the Venezuelan colonel-turned-oil-sultan is the most powerful and fascinating political alliance in the Americas. Five years before becoming president in 1999 and two years after a failed coup attempt, Mr. Chávez was released from prison and flew to Havana in hopes of meeting his revolutionary hero. Waiting to welcome him at the airport was the man himself. It’s been a lovefest ever since, with Mr. Chávez declaring that Venezuela is sailing in Cuba’s “sea of happiness.”

More crucially, after Cuba lost its Russian patron and plummeted into economic free fall, Mr. Chávez gave his friend one of the most magnanimous gifts in history — around 100,000 barrels of oil every day, gratis, with no strings attached — for as long as Cuba wanted it. In exchange, Mr. Castro sent thousands of doctors to Caracas — a deal derided by some critics as “oil for ointment.” No one doubts who got the better deal.

Unlike the quid-pro-quo-demanding Soviets, who picked up most of Cuba’s tab for three decades, Mr. Castro now receives adoration from a leader who happily calls him “mi padre.”

Not without reason. In 2002, when a coup appeared to have dislodged Mr. Chávez from power, it was Mr. Castro who spent night after night on the phone, tutoring his charge in a strategy to regain power and dispatch his enemies. “Don’t resign! Don’t resign! I kept telling him,” Mr. Castro recounted in his autobiography.

Since then, Ramiro Valdés, Cuba’s pre-eminent policeman and spymaster, has made Caracas a second home, reorganizing Venezuela’s military, police force and Internet services (a fiber-optic cable connects the two countries like an umbilical cord). Cuban advisers are dotted throughout Venezuela’s ministries, offering counsel on everything from literacy to opposition movements and elections. There will not be another coup, or many more elections.

“Deep down,” says the Venezuelan convalescent in chief, “we are one government.” They don’t call it “Venecuba” for nothing.

Hence, if the health of either man further fails — and both are walking the razor’s edge — all bets are off. One cannot overstate the symbolism that surrounds Fidel Castro in Latin America; Mr. Chávez’s legitimacy as a Bolivarian revolutionary depends, in large part, on his being mentored by Mr. Castro. And if Mr. Chávez succumbs to illness or is (somehow) voted out, Cuba’s oil spigot could well be turned off by a less generous successor. Raúl Castro, who is trying to salvage Cuba’s bankrupt economy with all manner of fixes and reforms, is especially dependent on Venezuelan munificence.

Despite the ailing titans, change is happening in Cuba — in ways big and small and previously unthinkable. Take for instance the marriage of a transsexual woman and an H.I.V.-positive gay man on Mr. Castro’s birthday. Hailing it as their “gift” to him, the happy couple cruised in a convertible through Havana, where gay men could once be hauled into work camps for being “anti-revolutionary.” The bride had her sex change surgery at the National Center for Sexual Education, run by Mariela Castro Espín, Raúl Castro’s free-spirited daughter, who has turned Havana into the San Francisco of the Caribbean.

Tolerance for entrepreneurship is also increasing. Cubans will soon be able to sell their homes, for the first time since the Castros took power. And the Obama administration has lifted many of the pointless and onerous restrictions on travel to Cuba.

Of course, if Marco Rubio, the hard-line Cuban-American senator from Florida, snares the vice-presidential slot for the Republicans, Democrats will feel pressure to tighten the screws of the embargo once again. And should the Republicans prevail in 2012, relations will almost certainly return to the Stone Age of nonengagement — hinged on the mantra that “Fidel will go any day now.”

While he appeared frail and off balance during his one brief “live” appearance at the Communist Party powwow in April, I would argue against any bet on Mr. Castro’s date with his maker. A worthy rival of Lazarus, he has survived three major surgeries and the loss of a good deal of abdominal viscera, not to mention the administrations of 10 United States presidents.

Certainly, there are enough family members in key government ministries — most notably Raúl Castro’s powerful son and sons-in-law — to ensure a degree of dynastic rule into the future. But the lavish concern and solicitation of the elder Mr. Castro toward his Venezuelan charge suggests a deeply felt fear should his island lose Mr. Chávez’s patronage.

That said, in case Mr. Chávez slips his mortal coil before his Cuban ally does, the über-strategist Fidel Castro has no doubt cobbled together some sort of contingency plan — as he was forced to do after the Soviets pulled out. Trust and sentimentality are not part of his political credo. Discussing an early betrayal by a compañero turned informer, Mr. Castro said he learned a crucial lesson: “You shouldn’t trust someone just because he’s a friend.” Or depend on him.

“Fidel is a force of nature,” observed his friend the writer Gabriel García Márquez. “With him, you never know.” Or as they lament in Miami, “Immortal until proved otherwise.”