The risk of developing autism may be passed on through - and not just to - future generations, researchers say.
The international study suggests older fathers are more likely to have grandchildren with autism than their younger counterparts.
The mechanism is unclear but it is thought they may transmit "silent mutations" to their grandchildren.
But experts have urged caution, stressing autism is the result of many different factors.
The study, looking at almost 6,000 people with the condition, is published in the journal Jama Psychiatry.
According to the National Autistic Society, more than one in every 100 people in the UK have the condition.
Previous studies suggested older fathers may be at greater risk of having children with autism than younger dads.
But the team of UK, Swedish and Australian researchers say this is one of the first pieces of evidence to show the risk can be passed on through - rather than just straight to - future generations.
The "silent mutations" - changes in genetic material - are likely to have no obvious impact on older fathers' own children, but they may build up through subsequent generations, or interact with other genes and environmental factors, to increase the chance of their grandchildren developing the condition, the researchers say.
Using national databases from Sweden they studied almost 6,000 people diagnosed with the condition and more than 30,000 without, tracking their parents' and grandparents' ages.
They found men who had a daughter when aged 50 or older were 1.79 times more likely to have a grandchild with autism, compared to men who fathered children when aged between 20-24.
And those who had a son when 50 years of age or older were 1.67 times more likely to have a grandchild with the condition.
But they say this study should not discourage older people from having children as though the risk is increased, it still remains small.
Co-author of the study, Dr Avi Reichenberg from King's College Institute of Psychiatry, told the BBC: "It is about choices. If you choose to have a child at an old age there might be consequences. This is something everyone should consider.
"Unfortunately we can't put exact figures on this risk yet. But most children born with older fathers and grandfathers grow up fine.
"And as scientists this type of information helps open doors to understanding more about the condition."
Caroline Hattersley, of The National Autistic Society, said: "While this research is useful in aiding our understanding of autism's complex causes, it should be treated with caution.
"Autism is thought to be the result of many different underlying physical and genetic factors.
"The study is not definitive, as we know that many people who had children at a young age also have grandchildren with the condition. We therefore urge parents and those thinking of starting a family not to be concerned about the findings."
Dr Terry Brugha, professor of psychiatry at the University of Leicester who was not involved in the study, said: "This is a solid piece of work and the findings are plausible. But as a grandparent or parent-to-be this is not something to be overly concerned about.
"We are at the early stages of research and this study gives us a slightly deeper understanding of what is going on in the background."