Sleep apnoea and snoring made conditions such as hyperactivity more likely later on, researchers said.
Lead researcher Dr. Karen Bonuck said the sleep problems could be harming the developing brain.
One estimate suggests one in 10 children regularly snores and two percent to four percent suffer from sleep apnoea, which means the breathing is obstructed and interrupted during sleep.
Often enlarged tonsils or adenoids are to blame for the conditions.
In adults, the result can be severe day-time tiredness, and some studies have hinted that behavioural problems such as attention-deficit hyperactivity disorder might be linked to the condition in children.

Dr. Bonuck, from the Albert Einstein College of Medicine at Yeshiva University in New York, said children with breathing issues during sleep were between 40 percent and 100 percent more likely to develop "neurobehavioural problems" by the age of seven.

She believes the sleep breathing issues could cause behavioural problems in a number of ways - by reducing the supply of oxygen to the brain, interrupting the "restorative processes" of sleep or disrupting the balance of brain chemicals.
She said, "Until now, we really didn't have strong evidence that sleep-disordered breathing actually preceded problematic behaviour such as hyperactivity".
"But this study shows clearly that symptoms do precede behavioural problems and strongly suggests that they are causing these problems", She remarked.