Some students are excluded from the National Education Longitudinal Study of 1988 (NELS:88) because of an inability, whether due to physical, mental, or linguistic barriers, to participate in studies requiring questionnaire or cognitive test completion. The implications of this exclusion for sample representativeness, national estimation, and policy studies are examined. Also described is a special study undertaken in the NELS:88 First Follow-Up to compensate in key respects for undercoverage bias related to such exclusion. The special study examined a subsample of 600 ineligible base-year eighth-grade students, collecting data on their enrollment status and demographic characteristics. Results obtained will allow calculation of a more accurate cohort dropout rate and will permit students who have become eligible (as through increased proficiency in English) to be taken into the study. Longitudinal studies similar to the NELS:88 must accommodate changes in eligibility as studies continue through 1992. In addition to a description of the NELS:88 and the Followback Study of Excluded 1988 Eighth Graders, recommendations concerning ways of reducing the numbers of excluded students are presented. Two figures illustrate the text. Four appendices provide the rationale and procedures for "sample freshening"; and exclusion criteria for the High School and Beyond Study of 1980, the National Assessment of Educational Progress of 1990, and the Base Year Ineligibles Study of the NELS:88 First Follow-Up. (SLD)