Here's a family finance problem that's growing more and more common as the divorce rate goes up.

A middle-aged man, divorced from his first wife, marries a younger woman and has children. Suddenly, he has the same type of life insurance needs as he had back when he was in his early twenties - namely, plenty of coverage to protect his young children in case he dies. But because of his age, life insurance is more than twice as expensive. What does he do?

I put this question to a number of life insurance agents, all of whom agreed that there's no easy answer. Many second marriages are so financially strapped that inadequate insurance is only one of several burdens. But they made these suggestions:

Many men hang on to the policies they bought when they were young, making the second wife the beneficiary on their employee group insurance. This solves the second-family problem, but leaves the first family without resources if he dies.

"I'm amazed at how often divorce lawyers overlook life insurance," says insurance agent John H. Ames of Morristown, N.J., "If the husband dies or becomes disabled, the first wife and children lose their support check, with no insurance proceeds to fill the gap."

If insurance is included in the separation agreement, arrange for part or all of the policies to revert to you as soon as the children if the first family are through college, or if your first wife remarries.

If your only obligation is child support, keep you whole-life policies for your second family and buy inexpensive decreasing-term coverage that expires when the child-support payments end.

If you're covered under an employe group-health policy, see if it's possible to buy additional amounts. Companies sometimes make extra coverage available at low cost, deducting the premium from your paycheck. You may not even have to pass a health exam, making this a possibility for people who are otherwise uninsurable.

When you leave the company or retire, this low-cost coverage expires. To convert to an individual policy with the same insurance company can be tremendously expensive. If you'll need insurance past the age you expect to retire, employee coverage should be supplemented with something else.

Look for organizations you can join that offer group term insurance. Professional socities, colege alumni groups and trade associations are just some the groups that sponsor low-cost policies for members. Generally these policies don't last past age 65.

One warning: Compare the cost of group coverage with the cost of individual term insurance. Group rates are sometimes higher, because of the average age or claims experience of that particular group.

Finance additional insurance by borrowing the cash value from your present whole-life policy. Loans from cash value are deducted from the policy proceed when you die, but you can keep the death benefit level by using the policy's dividends (if any) to buy extra term insurance.

"This looks good at 45," says Ames, "but by age 60 or 65, it looks awful," because of the high cost of term insurance and the big interest payment no cash value left and may not be on the policy loan. You have little or able to afford the annual cost.

Buy individual term insurance. For large amounts - says $50,000 or more - one-year renewable policies are less costly than five-year renewable term. For a man age 45, a $50,000 one-year policy costs around $250, says Ames: The rate increases a little every year; at age 60, that same coverage would cost around $1,000. 'I'd start a man out on all-term insurance," says Jack Bobo, insurance agent in Phoenix, Ariz., "since he needs a large amount of coverage. Later, I'd convert to whole-life." Term coverage ends at age 65 or 70.

Convert part of your term insurance whole-life if you'll need coverage past age 65 or 70. Whole-life is expensive; at age 45, a $50,000 policy would cost $1,000 to $1,500 a year (compared with $250 for term). At age 60, the price may more than double.