Asked to imagine the ideal person to take care of their children while they're at work, most parents would come up with a list something like this: a kind, firm, fun, motherly woman who would love her charges, yet not try to take the parents' place.

Parents want, in short, a Mary Poppins.

The demand for nannies -- although they're expensive and still difficult to find -- is exploding. Courtney S. Hagner and Robin D. Rice, who run Nanny Placement Services Inc. in D.C., estimate the demand for nannies -- due in part to older, successful, working mothers who can afford quality child care -- is 10 times greater than their supply.

Between 1972 and 1982, the number of first babies born to women in their early thirties more than doubled; the rate for women age 35 to 39 rose 83 percent.

Accompanying the trend is an increase in the number of schools and programs for training nannies, as more parents seek better credentials and standards in child care. Today's nannies are apt to be better educated, take their jobs seriously and are adamant in regarding their job as a profession, reflected in salaries, fringe benefits and respect.

Full-time, trained nannies earn about $800 and up a month, plus room and board, vacation and insurance.

Patricia Brown, 26, a graduate of the National Academy of Nannies Inc. (NANI), Denver, is one of the new breed of live-in nannies and proud of it. Even her license plate proclaims her status (and her alma mater).

For over a year, she has taken care of the infant twins of Cathy, a 37-year-old McLean attorney, and her 39-year-old husband, Al, a real-estate developer.

"I felt a little intimidated when I first came, Al having gone to Harvard and Cathy being a lawyer," admits Brown, who is from Michigan, "but they were open and honest. They said, 'Listen, we don't know anything about having kids so we're looking to you for that advice.' "

Brown, who joined the family when twins JoAnn and Steven were 5 weeks old, describes -- as do others -- the nanny/family relationship as a tricky one. "You're living with a family. They are not your parents; they are your employers. They are adults just like you, and you have to be able to communicate with them.

"It's not like working at Safeway, where if you get mad at the way things are being run, you can huddle together with the other employes and talk about it. You're the only one here so you need to deal with it."

In a previous job, Brown was unhappy when the mother refused to reinforce discipline of her charge, a 2 1/2-year-old child. "That gets real frustrating not only for the child," she says, "but also for the adults.

"When Mom was home, the little girl was doing things she would not normally do. I think she was almost challenging us -- 'Who's going to lay down the law? Who's in charge?' -- so that caused a lot of frustration."

To avoid such problems, Cathy, Al and Brown talk often and meet Thursday nights for what Brown calls their "weekly staff meeting." If the parents and nanny disagree, they ask the babies' pediatrician for advice.

"Privacy time" for the nanny is essential, says Brown, who works Monday to Friday, from when the children get up until their bedtime. She also cooks the evening meal and tidies up. Heavy cleaning is done by a housekeeper.

In spite of the strong demand for qualified nannies, some schools -- even those whose programs are widely acclaimed -- have gone out of business. Nanny Inc. in Chicago closed down last spring. When Peggy Dennis, formerly of the Foreign Service, tried to launch the Washington Institute for Nannies Inc., the 240-hour program did not attract sufficient students who could afford the near-$1,000 tuition. She is currently seeking funding.

Since fall 1983, George Washington University's Center for Continuing Education in Washington has been working on a 240-hour certificate "Child Care Specialist" program, for a tuition of about $2,000. But the necessary number of students has not yet signed up.

Says CCEW assistant dean Abbie O. Smith: "We had a tremendous amount of interest from people who were interested in taking the program and also from people who would say, 'As soon as you have a graduating class, I want to hire one' and even a couple of people who said they'd be willing to help pay the tuition of someone who's trained.

"Although interest was high on both sides, we found that we couldn't get enough to start a class . . . We realize that what we need to do is get some funding because the people interested in attending don't have the tuition dollars." CCEW plans to seek funding for student aid from foundations and individuals.

But despite obstacles, some nanny schools have succeeded, and more are being opened. In varying degrees, most programs cover child development, discipline, health and safety, nutrition, psychology and nanny-employer relations.

NANI, Brown's alma mater, which opened in June 1983, is thriving. "We are doing extremely well," says founder Terri Eurich, 34. "We started slow; we're building momentum. We put through 40 students in the first year, which I think is phenomenal."

Eurich attributes some of her success to the stringent curriculum and business requirements set up by the State Board for Community Colleges and Occupational Education, which regulates private schools in Colorado. In many states, such schools are not -- if at all -- well regulated.

NANI's tuition is $2,250 for 1,000 hours of course work, which is completed in 7 1/2 months. Most students are from out-of-state. Room and board is provided in nearby homes in exchange for 20 hours a week of child care.

"The benefits are mutual," says Eurich. " The families are not expecting a full-fledged, certified nanny at the beginning of the program, and they are willing to work with us and the students. It allows them some very well-screened and highly motivated child care." The graduates have "a built-in good reference" when they look for a full-time position.

Almost all of NANI's students pay their own tuition. Those who pay their own way, observes Eurich, are "committed" and can choose to work anywhere after graduation. NANI's students have ranged from ages 19 to 44 and include a graduate of Smith College who majored in Russian civilization and worked with computers, a school teacher, a librarian and a grandmother. The average salary of the January 1984 class was $930 a month, plus room and board, two weeks paid vacation and major medical.

Among problems other nannies and educators say they've encountered:

* Parents wanting Mary Poppins with degrees in early childhood education and nursing, for low wages.

* Parents wanting a nursemaid who also will cook and clean house.

* The high cost of tuition.

* Lack of regulations or professional guidelines to help nanny-school operators become established.

At the outset, many nannies and parents find it a good idea to set up ground rules on discipline, philosophy, authority and more. When questions of discipline come up, "I really rely on Patty's experience," says Cathy. "I tend to bow to her because I know she loves the twins and I think maybe she can be more objective . . ."

"She takes her responsibilities and her job as seriously and performs them as well as anybody I've ever come across," says Al, "whatever their title or their role."

Says former Montanan (and D.C. nanny) Christine Philipps, a college graduate in education who went on to become minority chief clerk for the Senate Judiciary Committee: "They were the mayor and you were the police" in discipline matters . Philipps, 26, stresses the importance of the mayor backing up police actions.

Sandy, a 23-year-old nanny, who was a pediatric nurse before becoming a nanny to 3-month-old twins in D.C., keeps a written log, talks nightly with the parents and meets formally with the parents once a week.

"It's a concern when the mother works," she says. "They don't want the babies to forget them. I spend a lot of time telling the parents things . . . what to expect so that they don't feel like they are out of it."

Meanwhile, Patricia Brown, who recently signed a second one-year contract, points to another not unusual nanny concern: becoming too close to the family. Although she says she feels "very relaxed" around Cathy and Al, she has to remind herself that they are her employers and she is doing a job. "I really love these babies. I think it's going to be real hard to leave this family when I do leave."