It was never a problem for Ozzie and Harriet.

As television's typical American family" of the '50s and '60s, it's a sure bet they didn't stay awake until 3 a.m. "discussing" whose turn it was to do the laundry.

But if the Nelsons represented today's average couple, there's a 50 percent chance Harriet would be earning a paycheck. And Ozzie would be doing some housework.

"According to our new sex-role consciousness," note Pat Koch Thaler and Hilary Ryglewicz in their book ("Working Couples"), "when both members of a couple become responsible for earning income, both become responsible for making it work at home as well."

Couples divvy up household chores in a variety of ways, says Thaler, who plans and administers programs for working adults at Marymount Manhattan College in New York.

"A lot of couples have worked out various kinds of informal contracts. Some divide responisbility according to who does what best, or according to their schedules.

"some make up little rules, like at my house the person who leaves last makes the bed. Other couples have a more casual division of labor and just pitch in to do whatever needs to be done."

But whatever the arrangement, says Thaler, "The issue of who does what at home in a dual-income family is a potential area of stress. I don't think couples split up over a conflict in who takes out the garbage, but it can add fuel to the fire if there's any trouble in the relationship."

Although there seems to be more attention lately on male participation in running the home, California sociologists Richard and Sarah Berk contend "husbands do zilch."

"Nothing much has changed," says Richard Berk, since 1975 when he and his wife surveyed a representative sample of 750 American homes where both the husband and wife were present. (About 40 percent were dual-income couples.)

"In most households there was an 80-20 split (women doing 80 percent of the household maintenance and men doing 20 percent)," he says. "If there are two wage-earners, usually the woman gets up a half-hour earlier than the man to get started on the household chores."

One ploy, he says, "is that husbands will feign incompetence. But if he can earn a living, he can run a washer and dryer."

Berk conceeds, however, that in many cases the husband does less housework "because the cards are so stacked against equity in a household. It's not a question of beliefs or ideology, but of our being so used to doing things in a traditional manner. Everything -- from the P-T-a to repair people -- is set up for women who stay in the home. I think it takes a really heroic commitment to change."

Part of the problem also can be traced to some women's reluctance to give up the decision-making power that accompanies being "in charge" of the house.

Says Wellesley College researcher Laura Lein: "Both husbands and wives have difficutlty relinquishing responsibility for their primary role in the family as breadwinner (he) and homemaker (she).

"One husband and wife said that as they tried to work out an arrangement for sharing responisibility for the household tasks, the wife took on this incredible ability to see dirt."

"If she stands over me and corrects me whenever I try to cook," notes one husband, "you can bet I'm going to stay out of the kitchen."

In other families, women resent being "the one responsible for managing the household," say authors Thaler and Ryglewicz. "For many a working woman, the concept of her mate's contribution to the household as 'help,' is unacceptable.

"While sharing the work is important, sharing the sense of responsibility for the home can be equally important."

One way to solve this problem, writes Caroline Bird in "The Two-Paycheck Marriage," is for the couple to sit down and "itemize the services they regard as essential, split those and discard what they can do without."

She suggests each person keep a personal diary of all non-job, non-leisure tasks performed in one week. Sort these tasks into two lists: 1) personal maintenance (going to the doctor, fixing a meal when eating alone); 2) household maintenance (food shopping, fixing the car, caring for children).

"Household tasks must be defined and assigned," says Bird. "Rembember they are not a moral , but a political issue. They have to be negotiated like a contract or treaty.

"She may want the windows washed every month, while he doesn't care if he can't see through them. He may want a big Christmas party she doesn't want. The trick is to agree on everything that has to be done -- and how well -- and then write it down in black and white."

Thaler and Ryglewicz add these guidelines for couples:

1. Don't try to do everything . Focus on what can and must be done. Set priorities according to your personal needs, and distinguish between what you wish you could do and what you really can do.

2. Be clear with each other about what you consider essentials . Take each other's needs into account, but elimate relationships and acitivites that are neither necessary nor gratifying. Experiment to find out what you can give up and what you really want to keep.

3. Identify who is going to do what . Either informally or with a written contract.

4. Let each do the work he or she finds most gratifying, or least objectionable .

5. Be flexible and prepared to change . If your system isn't working well, renegotiate as needed, and ask for help before you feel exploited.

6. Provide pressure-free space and time . Don't let yourself always be in a hurry; find time to enjoy yourself.

7. Get help . Use "personal-service" businesses to walk the dog, or to do other chores for which neither person has time or energy.

8. Live near a take-home Chinese restaurant .