by Susan Chira

About the author: Susan Chira is a freelance journalist.

First, Annie and Ivan married.

They had two children. They divorced. Later, Barry moved into Annie's house. Annie loved him. Her children did not. Three years passed, and he was gone. Two years later, Annie moved her children into Lee's house. Annie loved him. Her children did not.

For nearly three years, Annie and Lee and her children have circled one another warily, trying to decide whether this newest family could endure.

Annie's children, like countless across the country, are part of an increasingly common American family—the one that is formed, shattered, reformed and shattered again in the wake of repeated divorces and breakups. These children struggle to navigate a bewildering succession of stepparents, stepsiblings and live-in relationships that have no formal name.

Researchers who follow these children say...