This longitudinal study investigated two issues regarding child poverty dynamics: whether long-run transitions out of poverty have changed and whether the events associated with exits from poverty have changed over time. The study contrasted mobility patterns of young children over the 1970s with patterns over the 1980s, examining which poor children had higher or lower mobility prospects and whether those mobility prospects changed over time. Finally, the study investigated how changes in family structure and in receipt of welfare income related to exits out of poverty and how they changed over time. Data came from the Panel Study of Income Dynamics, which gathers longitudinal information on offspring of the original 1967 sample of 5,000 families. Data analysis indicated that about half of the children who were in poor families at the start of each decade remained poor. For African American children and children in female-headed households, both the relative and the absolute mobility were considerably lower. Because there were no significant changes in mobility over time, the study concludes that there is no evidence that the increase in inequality during the 1980s, which contributed to the rise in poverty, was offset by an increase in mobility. Seven tables are included. (SM)