Incomplete data on trait values may bias estimates of genetic and environmental variance components obtained from twin analyses. If the nonresponse mechanism is ‘ignorable’ then methods such as full information maximum likelihood estimation will produce consistent variance component estimates. If, however, nonresponse is ‘nonignorable’, then the situation is more complicated. We demonstrate that a within-pair correlation of nonresponse, possibly different for monozygotic (MZ) and dizygotic (DZ) twins, may well be compatible with ‘ignorability’. By means of Monte Carlo simulation, we assess the potential bias in variance component estimates for different types of nonresponse mechanisms. The simulation results guide the interpretation of analyses of data on perceptual speed from the Swedish Adoption/Twin Study of Aging. The results suggest that the dramatic decrease in genetic influences on perceptual speed observed after 13 years of follow-up is not attributable solely to dropout from the study, and thus support the hypothesis that genetic influences on some cognitive abilities decrease with age in late life.