A study found babies born after 42 weeks were more likely to suffer behavioural problems such as ADHD in early life.
Most UK mothers are induced before 42 weeks but pregnancies lasting beyond 43 weeks are not unknown.
Women should be aware of the risks of prolonging pregnancy, experts report in the International Journal of Epidemiology.
The research was carried out in The Netherlands, where until recently it was commonplace for women to choose not to be induced if they were overdue.
A study of more than 5 000 babies found those born after 42 weeks were more likely to develop behavioural problems than those born around their due date, and had more than twice the risk of Attention Deficit/Hyperactivity Disorder (ADHD).
Lead researcher Dr Hanan El Marroun from the Department of Child and Adolescent Psychiatry at Erasmus MC-Sophia in Rotterdam said post-term as well as pre-term births seemed to be associated with long-term health effects.
She said “Every pregnant woman knows that if the child comes early that’s not good, so why don’t we question the long-term effects of when a child comes too late?”
In the UK, guidelines state than women should be induced between 41 and 42 weeks, and warned about the possible complications if they wish to prolong pregnancy.
Complications include a higher risk of stillbirth and difficulties in delivering large babies.
However, a minority of women, dubbed “the 10-month mamas”, believe a baby will come in its own time and avoid medical intervention.
Dr Virginia Beckett is a consultant in obstetrics and gynaecology and a spokeswoman for the Royal College of Obstetricians and Gynaecologists.
Commenting on the study, she said: “In the UK it is unusual for women to go beyond 42 weeks. Some people choose to go beyond 42 weeks and our advice would be they increase their risk of stillbirth and other complications.”