A study of 5,000 babies born in Rotterdam between 2002 and 2006 found those who were born at 42 weeks gestation or more were at higher risk of significant behaviour problems and were twice as likely to have ADHD at age three.
In 2009 there were more than 28,000 babies born at 42 weeks gestation or more in England and Wales.
It is not clear if the behaviour problems were caused by being overdue or both factors were influenced by something else.
Lead author Hanan El Marroun, said: "Post-term children have a considerably higher risk of clinically relevant problem behaviour and are more than twice as likely as term born children to have clinical ADHD.
"Further research is needed in order to determine the causes of post-term birth and to minimise the long-term consequences. It is also important that further research is carried out in order to demonstrate a causal relation between post-term birth and behavioural problems and longer follow ups would also be advantageous.”