Couples in the second half of life are rewriting the terms of their relationships. Rather than marry or live together, many of them have separate homes and see each other several times a week, or three times a month; they often say they are highly committed to each other but want personal space and independence.

With the rise of “gray divorce,” and a doubling of the divorce rate for those 55 and older, there is a larger pool of single adults who may want a long-term partner, and want to make to it work without entangling finances or relationships with adult kids.

It’s a “new frontier in partnered relationships,” says Susan Brown, a sociologist and co-director of the National Center for Family and Marriage Research at Bowling Green State University, in Ohio.

Dr. Brown found in a survey of 2,166 adults ages 50 to 65 that nearly one-third of those in an unmarried relationship were in a committed long-term relationship but living apart—an arrangement academics often call “living apart together” and one that Dr. Brown expects to become more prevalent.