This study examined changes in low-income children's living arrangements over time. Caregivers of children in Boston, Chicago, and San Antonio completed interviews in 1999 and then again 16 months later as part of the Three-City Study of low-income families with children. The percentage of children living with single mothers who were not cohabiting or married declined from 57 to 54 percent between interviews. The percentage of children living with mothers and their cohabiting partners increased from 8 to 10 percent, while the percentage living with mothers and their married partners increased from 26 to 28 percent. Virtually all cohabiting and marriage that began between the first and second interviews involved a mother and a man who was not the child's biological father. About 42 percent of mothers who were cohabiting at the first interview had ended the relationship by the second interview, and 16 percent had married. About 18 percent of mothers who were married at the first interview had separated by the second interview. Overall, 22 percent of children had experienced changes in their caregivers' living arrangement during the interval. Approximately 44 percent of parents who began cohabiting or were married between interviews had not received welfare since the passage of national welfare reform legislation in 1996. (Contains 28 endnotes.) (SM)