ADHD can manifest itself in a number of different ways, from poor concentration and extreme hyperactivity to interrupting and intruding on other people and not being able to wait in queues.
And the practice - which will dismay some campaigners - already has a strong following the UK.
Children with attention deficit hyperactivity disorder (ADHD) are commonly given Ritalin, a stimulant drug designed to improve concentration levels.
Opponents say they have unpleasant side-effects, reducing some children to a "zombie-like" state, and claim some parents, doctors and teachers are using the drug to cancel out perfectly natural childhood boisterousness and creativity.
But the research, carried out in just one US state, suggests that many are also being given the anti-depressant Prozac or similar drugs in a class called SSRIs.
The use of Ritalin in the US is high - more than one in ten children between the ages of six and 14 studied were receiving the drug.
But the researchers also found that the number taking combinations of different drugs had risen sharply in the last decade.
ADHD can manifest itself in a number of different ways, from poor concentration and extreme hyperactivity to interrupting and intruding on other people and not being able to wait in queues.
Dr Jerry Rushton, the lead author of the study, presented to the annual meeting of the American Academy of Paediatrics, expressed concern.
"New drugs nearly always experience a rise in prescriptions over the first few years of their lifespan, but the consistent increase in SSRI use and in dual prescriptions is especially surprising.
'Overprescription'
"We need further information about whether this is due to new unrecognised mental disorders, substitution for other therapies, or overprescription."
However, one UK psychiatrist - a firm supporter of Ritalin - says that there may well be occasions in which extra drugs are needed to help children.
Dr Finn Cosgrove, who runs a private clinic in child psychiatry, said: "You may have a situation in which a child's ADHD is improved using Ritalin, but who is still showing obsessive compulsive symptoms.
"You cannot simply not treat those symptoms, and there is no evidence that using two drugs in combination is harmful to the child."
He said that he would not choose to use Prozac in children, as its chemical components take a long time to leave the body.
And he denied that Ritalin could be responsible for reducing children to a "zombie-like" state unless too high a dose was given from the outset by the doctor.
"I always build up the dose gradually, so the body gets accustomed to the drug, and I have never seen these problems."
The use of psychoactive drugs on young children is still a controversial technique in this country, with many child psychiatrists prefering not to do so.
One problem with using even established adult drugs such as Prozac on children is that the best or even the safe dose for young people has never been fully established with a clinical trial.