One in five babies has symptoms that could lead to conditions such as ADHD, according to research published in Archives of Disease in Childhood.
The review of previous studies looked at nearly 17,000 children.
A child-health expert said it would be wrong for parents to be "overly alarmed" by the results.
Crying in babies is normal, but some cry "excessively" after the age of three months for reasons other than colic.
An international group of researchers looked at this as well as problems eating and sleeping.
By comparing data from 22 studies from 1987 to 2006, they found a link between these issues and problems later in life.
There was an increased risk of ADHD (Attention Deficit Hyperactivity Disorder), anxiety and depression as well as aggressive behaviour.
The research showed that a baby with more than one risk factor was even more likely to develop behavioural problems.
Professor Dieter Wolke, from the University of Warwick, told the BBC: "It is about a 100% increase in risk, a doubling of risk of behavioural problems with excessive crying, sleeping and eating problems."
Jane Valente, a consultant paediatrician at Great Ormond Street Hospital, said: "It would be wrong for people to get overly alarmed. I don't think on the basis of this report people should be going to their GPs.
"If a baby is not behaving like other babies it is probably worth discussing with a midwife or health visitor."
The study cannot tell if issues as a baby cause behavioural problems later in life: they could be an early symptom of those later problems.
Professor Wolke said while there were treatments for problem crying, feeding and sleeping in babies, there was no research assessing their impact later in life.
He added: "If you could prevent behavioural problems with an early intervention, in a public health-sense it could be very important."
Professor Mitch Blair, officer for health promotion at The Royal College of Paediatrics and Child Health, said: "It is an important study."
He said parents were very good at knowing when something was wrong with their children and that the study "really reinforces the need for attention at an early stage to prevent issues later in childhood".
Babies who cry excessively and have problems feeding and sleeping have a greater risk of serious behavioural problems later in life, say scientists.