FORTUNE — Dear Annie: A couple of months ago, my boss abruptly left the company, and I was promoted to his job as leader of a 16-person product-development team. This was somewhat surprising, since I am the youngest team member (I’m 27) and have been here for the shortest period of time (two and a half years).

It’s a great job and I’m delighted to have it, but several of my direct reports, who are twice my age or older, are not so thrilled. I’m trying not to let their wisecracks about my age get to me, but I am having a hard time getting them to take me seriously as their boss. So far, we’ve managed to get the work done despite the friction, but it’s tough. Do you (and your readers) have any suggestions for me on how to win them over? — Nobody’s Baby

Dear N.B.: Scant comfort though it may be, you’ve got lots of company. A survey last month by office-equipment maker Pitney Bowes found that about 20% of midlevel corporate employees now report to a boss who is younger than they are.

That figure seems set to climb: Almost half (45%) of manufacturing companies are trying to encourage workers in their 50s and 60s to stay on the job longer, so as not to lose their hard-to-replace skills and experience, according to a new poll of senior executives by Advanced Technology Services.

“It’s happening everywhere,” says Jim Finkelstein, president and CEO of a consulting firm called FutureSense, based in San Rafael, Calif., and author of a new book, Fuse: Making Sense of the New Cogenerational Workplace. Many of his clients are tech companies and family-owned businesses that bring him in to help resolve clashes between Baby Boomers and bosses they perceive as still wet behind the ears.

“Part of the reason for this big shift, of course, is that we Boomers were supposed to have retired en masse by now, to make room for the next generation of talent,” Finkelstein says.

A range of economic factors, from the ever-mounting cost of health care to the decline of defined-benefit pensions, has kept many people working longer than anyone (including Boomers themselves) expected.

“So the dynamics of different age groups at work have changed radically from even just a few years ago,” Finkelstein says. “Everyone is having to adapt.”

He has noticed in his consulting work that the generation gap shows up “even in seemingly minor details like office space. A video game company, for instance, might have a ‘wow’ workplace with pool tables, dogs under the desks, and everyone in blue jeans,” he says. “A Boomer hire will take a look around and say, ‘You can’t be serious.’”

It doesn’t help, Finkelstein adds, that people of different ages tend to stereotype each other. “There is a tendency to view young people as ‘slackers’ immersed in technology, with short attention spans and deficient people skills. Boomers get typecast as set in their ways and stuck in the past,” he says.

In practical terms, your task is “to let your older teammates know that you respect their experience while still asserting your leadership of the group,” says Finkelstein. Three ways to get on the right track:

1. Ask for feedback and suggestions.

“You never want to come across as a know-it-all, no matter what age you are,” notes Finkelstein. “That’s especially true when someone working under you may actually be more knowledgeable than you, in some areas.”

In addition to being a sign of respect that might smooth more than a few ruffled feathers, getting the benefit of another person’s experience can work to your advantage. “Seeking out information about what has worked, or not in the past could keep you from reinventing the wheel,” Finkelstein says.

2. You are in charge, regardless of your age.

“You earned your current position by proving that you’re capable of handling a managerial job. Don’t question your own authority,” Finkelstein advises. Employees who are older than you “aren’t your parents. You can actually tell them what to do,” he adds. In fact, sometimes you have to.

Some people (you may be one of them) resist that aspect of leadership. “Unless you’re bossy by nature, telling others what to do and giving them honest feedback on their performance is always a little awkward,” Finkelstein says. “It’s infinitely trickier when they are old enough to be your parents.”

If your personality type is such that you struggle with this, consider asking the human resources department if training is available for new managers (of any age). Almost all large organizations offer it since, after all, they have a vested interest in your success.

3. Keep the focus on the team.

As a manager, you’re responsible for keeping everyone’s attention on shared goals. “Instead of focusing on age differences — or any other differences, for that matter — among colleagues, constantly promote the idea that you are all working toward satisfying customers and making the whole enterprise more successful,” says Finkelstein. “That’s what counts. So don’t allow side issues to become distractions.”

It would probably help to recognize that, even when age is not an issue, learning to be a boss takes practice. After only a couple of months in the job, you may not yet feel secure enough in the role, which may in turn be causing your teammates to lack confidence in you.

The remedy for that: Time, and a few notable wins. “Concentrate on being a great leader,” Finkelstein says, “and the wisecracks will stop. Eventually.”

Talkback: Have you ever worked for a boss who was much younger than you? If you are a young manager, what has helped you gain the respect of older colleagues? Leave a comment below.