A complex interrelation exists between change in depression symptomatology and cognitive decline. Studies indicate either that depression is a direct risk factor for cognitive change over time, or vice versa. Longitudinal twin studies provide the possibility to unravel cause and effect of correlated traits. Here, we have applied twin modeling approaches to shed light on the genetic correlation between both level and change of depression symptomatology and cognitive functioning, and to further explore the bidirectionality of any such correlation using assessments of both phenotypes at two occasions 10 years apart. The study included 2,866 Danish twins with a mean age of 56.8 years at intake (range: 45–68 years). Of these, 1,267 were intact pairs. A total number of 1,582 twins (55%), of whom 557 were intact pairs, participated in the follow-up survey. We found stable cross-sectional heritability estimates of approximately 60% for general cognitive abilities and 30% for affective depressive symptoms. There was a considerable decline in the mean cognitive performance over 10 years, whereas the mean affective depression symptoms score was stable and with no genetic contribution to any individual change. Additionally, we saw a small but significant cross-trait correlation at both occasions (-0.11 and -0.09, respectively), but cross-trait cross-occasion analysis revealed no evidence that either of the two traits predicts the other over a 10-year interval. Thus, our study was not able to detect any causal association between change in depressive symptomatology and cognitive decline in middle-aged and elderly people over a 10-year interval.