Background: There is an absence of population-based long-term studies on the risk of neurological sequelae in children born after in-vitro fertilisation (IVF). Our aim was to compare the frequency of such problems between IVF-born children and controls. Methods: We did a population-based retrospective cohort study in which we compared development of neurological problems in 5680 children born after IVF, with 11 360 matched controls. For 2060 twins born after IVF, a second set of controls (n=4120), all twins, were selected. We obtained data on neurological problems from the records of the Swedish habilitation centres. Findings: Children born after IVF are more likely to need habilitation services than controls (odds ratio 1.7, 95% CI 1.3-2.2). For singletons, the risk was 1.4 (1.0-2.1). The most common neurological diagnosis was cerebral palsy, for which children born after IVF had an increased risk of 3.7(2.0-6.6), and IVF singletons of 2.8 (1.3-5.8). Suspected developmental delay was increased four-fold (1.9-8.3) in children born after IVF. Twins born after IVF did not differ from control twins with respect to risk of neurological sequelae. Low-birthweight and premature infants were more likely to need habilitation than fullterm babies. Maternal age did not affect risk. Interpretation: Our study suggests that children born after IVF have an increased risk of developing neurological problems, especially cerebral palsy. These risks are largely due to the high frequency of twin pregnancies, low birthweight, and prematurity among babies born after IVF. To limit these risks, we recommend that only one embryo should be transferred during IVF.