Objectives To investigate changes in children’s television and computer time according to three socioeconomic status (SES) indicators. Design Prospective cohort study. Methods Data were drawn from the European Youth Heart Study and included longitudinal data collected in 1997 and 2003 in Denmark. Television and computer time were self-reported by children. Parental education, income and ethnicity were parent-reported. Baseline data were available for 549 children (47.0% boys, 9.6 years). Generalized linear mixed models analyzed whether changes in television and computer time from baseline to follow-up differed according to the SES-indicators. Result TV viewing time increased with 25% over time (ExpB = 1.25, 95% CI = 1.04–1.50). At both time points, children with two higher educated parents viewed 25% less hours of television than children with no higher educated parents (ExpB = 0.75, 95% CI = 0.60–0.94) and one higher educated parent (ExpB = 0.75, 95%CI = 0.59–0.97). Among children with no higher educated parents the odds of being in a higher category of computer time increased with 80% over time (OR = 1.80, 95% CI = 1.24–2.60). Among children with two higher educated parents the odds of being in a higher category of computer time decreased with 45% over time (OR = 0.55, 95% CI = 0.32–0.94). The association with ethnicity showed that white children had 42% lower odds (OR = 0.58; 95% CI = 0.34–1.00) of being in a higher category of computer time than non-white children. No significant associations were found for parental income. Conclusions The most important SES measure of screen-based behaviors in children was parental education. Ethnicity was only associated with computer time. Financial resources were less relevant for changes in television viewing and computer use.