Southwest Airlines Co., the world's largest low-fare carrier, said its chairman, president and chief executive, Herbert D. Kelleher, has prostate cancer and began radiation treatment today.

Kelleher, 68, said the cancer was discovered during an annual exam, and he will receive brief treatments on weekdays for about two months while he keeps working. His colorful promotions of Southwest, such as shimmying in an Elvis Presley-style jumpsuit for a magazine cover, have made him a high-profile chief executive.

The diagnosis highlights the lack of a clear successor at an airline whose co-founder and holder of the carrier's top three jobs has reached an age when many executives are retired, a key weakness for a company even if the leader is healthy.

"It's likely the board will reconsider" and announce a second-in-command, said Buckingham Research Group analyst Helane Becker, who has a "buy" rating on Southwest shares. "There's an excellent depth of management."

Analysts have speculated about who will succeed Kelleher, whose current contract runs through 2000. While he has no publicly declared successor, "the top four or five people at the company are all very able executives who've been with company for long time and will continue to run the company," Becker said.

Kelleher become chairman in 1978 and took the titles of chief executive and president in 1981. While Kelleher said he may experience a loss of energy in the last two weeks of the treatment, he saw no need to announce the executive next in line.

"There is no need to update any succession plan because our board discusses that issue on a regular basis and has done so for a good number of years," Kelleher told reporters in a conference call. "Insofar as we know, it's not going to involve any disruption or even any interruption in Southwest Airlines. So it doesn't change anything."

The company's stock fell 12 1/2 cents a share today, to $16.37 1/2. While the shares have slipped in the last few weeks partly on concern that rising fuel costs will hurt earnings, Southwest stock has risen 20 percent in the past 12 months.

Since drawing up Southwest's original flight plan--a triangle with Dallas, Houston and San Antonio at its corners--on a cocktail napkin, Kelleher has become the embodiment of the airline and its culture.

He defeated the head of a smaller rival in an arm-wrestling contest to settle a dispute over a marketing slogan. A leather-clad Kelleher rode a Harley-Davidson motorcycle to an employee party.

The executive has developed a loyal following among employees because he gives them broad latitude. He also has been known to spend one day a month helping baggage handlers load luggage on planes.

Kelleher wants to remain at the company after his current contract expires. "I have every intent and every desire to remain at Southwest Airlines at the expiration of my contract, but ultimately that's at the discretion of the board," he said.

Kelleher's health and a lack of a declared successor were on the agenda at the company's shareholders' meeting in May, when stockholder J. Michael Schaefer unsuccessfully proposed stripping Kelleher of one or more of his titles to spread the responsibility of leading the company.

Schaefer's proposal for shareholders, which was automatically scrapped because he didn't appear at the meeting to present it, said Kelleher's "longevity is speculative, he being a chain smoker . . . and a frequent flier." It continued: "Unless nudged by the shareholders to divide his control and responsibility, he simply won't do it."

Though Schaefer didn't attend the meeting, Kelleher still addressed the issue with his trademark humor. Asked if he smoked too much, Kelleher replied, "I smoke the appropriate amount," with a favored Merit cigarette dangling from his lips. He smoked throughout the annual meeting and a press conference.

While smoking isn't considered a direct cause of prostate cancer, the issue focused on Kelleher's importance to Southwest.

Kelleher's doctor, Andrew C. von Eschenbach, said "because of his adherence to a regular examination and testing regime, his prostate cancer was discovered at a relatively early and fairly mild stage of development." The doctor said he had the "full expectation that Herb will continue to lead a fully active and productive life just as if he had never had prostate cancer."

Kelleher also joked about the daily treatment regimen at MD Anderson Cancer Center in Houston, which will force him to forgo extended trips. "Our officer group is probably somewhat disappointed that I will be in my office more than normal during the treatment period, since ordinarily I travel several days per week."

CAPTION: Southwest Airlines chief Herbert D. Kelleher has prostate cancer.