Retirement? What retirement?

New Corp. founder Rupert Murdoch just hit 80. Viacom and CBS topper Sumner Redstone turns 88 on May 27. But neither mogul seems about to relinquish his perch atop a media empire.

Neither corporation has publicly laid out succession plans for investors and shareholders. Both patriarchs have muddied the waters by bringing children into their companies even as they have hired strong non-family members as their top execs — leaving Wall Street watchers to fill in the blanks with speculation.

Their question: what happens when the two empire builders leave the scene?

Succession issues aren’t the only thing that Murdoch and Redstone have in common. Their business and personal lives bear some striking resemblances.

Murdoch, heir to a newspaper in a small Australian city, built a worldwide empire, News Corp., with interests in publishing (London Times, Wall Street Journal), TV (BSkyB, Fox’s broadcast and cable nets), film (20th Century Fox) and new media (MySpace, the Daily). Redstone, heir to his father’s theater chain in Boston, National Amusements, built it into a global business that includes Viacom (MTV Networks, Paramount) and CBS (CBS Network and stations, Showtime, Simon and Schuster).

Murdoch had one child, Prudence by his first wife, Patricia, whom he divorced after a decade of marraige. His second marriage to Anna resulted in three children — Elisabeth, Lachlan and James — who at various times have been considered his corporate heirs. That marriage ended in divorce after 32 years. Murdoch is now married to his third wife, Wendi Deng, 38 years his junior, with whom he has two young daughters.

Redstone’s marriage lasted 55 years and yielded two children, Shari and Brent. It ended in 1999, and shortly thereafter Redstone married a former primary school teacher 39 years younger than him. That union ended in 2009.

Both moguls have had stormy relationships with their offspring.

Redstone has feuded with daughter Shari, 57, who sits on his companies’ boards and is president of theater chain National Amusements, over corporate governance; his son Brent, 60, sued him in 2006, alleging that his father favored rising star Shari while keeping him out of the business.

Murdoch’s most public dispute has been with eldest son, Lachlan, 39, who once held executive posts at News Corp. in New York and was seen as his heir apparent but resigned abruptly in 2005. He moved to Australia, where he owns and runs a private equity firm. He also acquired an ownership stake in Australia’s Ten television network in October, which he’s now overseeing.

Lachlan has been considered out of the running for CEO, but some say he could still end up playing an important role at the company.

Daughter Elisabeth, 42, worked briefly at News Corp. but left after quarreling with another exec and became an entrepreneur. Her venture, U.K. production shingle Shine, bought Ben Silverman’s Reveille for $125 million three years ago. The studio produces such international hits as “The Biggest Loser” and “Masterchef.”

News Corp. recently bought Shine, a move that brought Elisabeth back into the family fold.

“Some people on Wall Street have been very critical of the Shine acquisition, saying that News Corp. overpaid for the asset,” says one analyst. “But I think she’s a pretty impressive executive and she’s shown that she’s adept by building one of the larger TV production studios in Europe.”

While Elisabeth may have plenty of business and programming experience, she’s not expected to win the top job — a post that youngest son, James, 38, seem best poised to inherit.

“He’s the most likely candidate” to run the company, says David Joyce, an analyst at Miller Tabak.

In March, James was promoted to News Corp.’s deputy chief operating officer as well as chairman and CEO of the company’s international operations and relocated to New York. Many analysts saw that move as the clearest sign yet that James will end up running it all, although not necessarily soon.

Instead, many analysts expect James to work closely with COO Chase Carey, who is widely admired by Wall Street for leading News Corp. through its recent tough negotiations to get cable operators to pay higher license fees for the privilege of carrying Fox.

“I picture Chase being CEO for a long time,” says Joyce. “He definitely has the business and negotiating acumen and experience. Shareholders would like to see him continue as the lead executive.”

Carey aside, of all the Murdoch offspring, James is seen as the one with the most operating experience. He previously ran London-based satellite TV operator BSkyB, for which News Corp. is now negotiating with the company’s board of directors and British regulators to own in full. His experience running Star TV, News Corp.’s Asian TV interests is also a major asset.

A few analysts say they could envision a scenario in which James would run the TV and satellite distribution and operations assets; Elisabeth, the programming assets, including the film and TV studios and the Fox network; and Lachlan, the newspapers, including the New York Post, Dow Jones and the Wall Street Journal.

“There’s plenty of industry buzz about Rupert getting his kids to sit down and grasp that this is their future and their legacy,” says Joyce.

Over at Viacom, succession plans are similarly thorny.

In the past, Redstone has shown a taste for shoving heirs apparent out the door: Frank Biondi (1996), Mel Karmazin (2004) and Tom Freston (2006).

Daughter and board member Shari seems out of the running because of her publicly rocky relationship with her father.

Instead, Redstone’s real heir apparent — at least for now — appears to be the company’s current president and CEO, Philippe Dauman, 57, who has served in that role since September 2006, his second go-round at the company.

Since he and Tom Dooley, the company’s COO and Dauman’s longtime second in command, have taken the reins of Viacom, the stock price has risen steadily since the recession brutally hit broadcasters in 2008-09.

For the six years prior to his posting at Viacom, Dauman was co-chairman and co-CEO of DND Capital Partners, a private equity firm specializing in media investments that he founded with Dooley.

Dauman’s return was no accident. From 1993 to 1998, he was Viacom’s general counsel. In 1994, he added the title of exec VP and became a member of Viacom’s executive committee. He served in both of those roles until he departed to launch DND in 2000.

“On a day-to-day basis, Sumner is far less involved and I don’t think Philippe is going anywhere,” says David Bank, managing director of equity research for RBC Capital Markets.

Dooley is seen as an important part of that package.

“I think they elevated Dooley in part to keep him and in part to make him a more important face to investors and to the public,” says Bank. “He’s really well thought of by the street and there’s a lot of confidence in him.”

Like Dauman, Dooley has done two tours of duty at Viacom. He first joined the company in 1980 and served as senior veep of corporate development, prexy of interactive television, VP of finance, treasurer and deputy chairman.

Succession aside, Murdoch and Redstone have built giant congloms that, as public companies, have taken on a corporate momentum of their own. While it may be hard for some investors to envision these empires without their leaders, the fact remains that solid management is in place. And now, with ad sales bouncing back, worldwide box office receipts holding steady and myriad new ways emerging for bringing content to auds and monetizing it, the two octogenarians could probably spend more time on leisurely pursuits and their coprorations would be none the worse for it.