Mary, a single working mom with an 8-year-old asthmatic daughter, was fuming.Worried about her child's complaints of abdominal pain, then in its second day, she had called her HMO primary care physician, only to learn she would have to wait three days for an appointment. She slammed down the phone and made a second call-to the HMO's complaint hot line.

All Mary (not her real name) wanted was to talk to a doctor-now.

One day, she may be able to get her wish. Especially if physicians like Brent Blue, MD, and Dave Mayor, MD, get theirs.

The two entrepreneurs have launched independent ventures aimed at remedying what they consider a major flaw in modern medicine: the inability of patients to speak to physicians at will. This communication gap leaves patients like Mary frustrated and sends countless others on needless, costly trips to the emergency department.

"There is no fundamental physician-patient relationship any more," insists Dr. Blue, founder of 2-1/2-year-old Doc Talk Inc., in Jackson, Wyo. "It can be immediately canceled by a change in insurance. Not only that, physicians don't have the time to talk to patients."

His "Dial-a-Doc™" service links 2 million eligible users to 260 physicians in 37 states on a seven-day, 24-hour basis. It's fielding 20 calls a day. Most tap in through corporate sponsors, who buy bulk access for their customers on a prepaid basis. He declines to say what the doctors earn.

"There are two ways to see a doctor: Make an appointment or go to the ER," adds Dr. Mayor, president of 1-year-old Ask-a-Doc Inc., in Burr Ridge, Ill. "I saw this as a gap to be filled."

The emergency physician's round-the-clock 800-ASK-A-DOC service is handling 10 daily calls, which are distributed among 20 doctors in five states. Paying by credit card, callers ante up $4.95 per minute or $29.95 for unlimited time. Doctors earn $2 for each minute of advice they give.

Although the two doctors have never met, they echo common themes. They do not disparage their competition, the burgeoning nurse advice lines set up by insurance companies. But they point out that these services-used by an estimated 18 million people in 1997 -- hold the nurses captive to predetermined scripts or protocols.

The two doctors bristle at they: detractors, who charge that giving anonymous, one-time advice to a caller does not constitute good medicine. "It's easy for a critic to take a pot shot," Dr Mayor says. Dr. Blue's qualifier: "We're not practicing medicine over the phone, we don't diagnose, don't prescribe, and don't treat."In contrast, Dr. Mayor permits his physicians to prescribe medicine over the phone, charging the caller $10 for the privilege.

About one caller in 20 seeks a prescription, typically for various antibiotics or cough suppressants. He dismisses as unrealistic professional opposition to phone prescribing.

Both services operate out of "virtual offices." Calls are routed through a central switchboard to physicians who reveal their identities at their discretion. They work out of their homes or offices in four- to 12-hour shifts.

"My physicians can't have patients scheduled at the same time," says Dr. Mayor, who concedes that this restriction depends on an honor system.

Marketing the service has proven difficult for Dr. Blue. His original idea was to sell prepaid debit cards to individuals. Although 10,000 cards are in circulation, the idea didn't catch on. "Individuals loved the service, but did not want to pay for it," observes Dr. Blue, who turned his marketing efforts to insurance companies.

The HMO market proved equally tough to crack for the family physician, who approached 100 carriers, including Cigna, Aetna and various Blue Cross plans. "The insurance industry wants to control everything that is said to their clients," Dr. Blue asserts. "it's a very difficult market to break into."

He went on to secure three contracts with private companies, including Advantage Marketing Systems, that sell nutritional supplements and market bundled corporate discount packages.

Meanwhile, Dr. Mayor's marketing efforts have been limited to billboards, radio and television in Chicago. Most of the calls thus far are from curiosity seekers who listen to a recorded preamble, but hang up before giving over their charge card numbers.

While the services are scrambling for customers, they won't have to turn far to staff the telephone lines. More than 1,600 physicians have applied to work for Dr. Blue's Dial-a-Doc™.