One consequence of following individuals over time in longitudinal studies is panel attrition, or drop out, an issue that presents modeling challenges for researchers. The implications of non-random dropout or attrition were studied. The data for this analysis came from the first and fifth waves of the National Youth Survey. The survey was administered to a national probability sample of youth ranging from age 11 to age 17 in 1976. The interest centers on the level of serious delinquency self-reported by a sample of 1,725 participants at the first wave of the survey administered in 1977 and the fifth wave administered in 1981. Serious delinquency is defined as including all of the “index offenses” except sexual assault. Sensitivity analyses show modest departures from a random dropout model can account for a substantial proportion of the within-subject decline in offending observed in longitudinal self-report studies. Results also show how one might be able to use the data to impose some plausible constraints on the analysis to achieve identification. Using one set of reasonable identification restrictions, the analysis suggests that within-subject declines remained while explicitly adjusting for the effects of attrition. There are at least three strategies for handling attrition problems in existing data sets: (1) imputation of the missing values with suitable estimates; (2) analysis of incomplete data without adjustment; and (3) discarding of non-respondents and calculation of weights for respondents to compensate for the loss of cases. Another useful tool is the practice of partially following up on hard-to-interview respondents. Three important future research efforts are described. The first project would involve an application of this methodological approach to a serious offender sample. The second project would examine the longitudinal relationship between age and victimization. The third project relates to the timing of dropout. 5 tables, 9 footnotes, 41 references