The study, published in the journal Child Development, looked at 357 adopted children and their families in the US.
A UK expert said parents needed to be more aware of the stress in their lives and how it affected their children.
The parents were interviewed when the child was nine months old and again at age 18 months.
They each completed a questionnaire to tease out the state of their relationship – were they stressed at work, less engaged at home, thinking about divorce?
They were also asked if their child had difficulty falling or staying asleep.
The researchers found that the strength of the parents’ relationship at nine months affected sleep patterns at 18 months.
Professor Gordon Harold, from the University of Leicester, and part of the international research group, said: “Regulated sleep is essential during infancy for healthy brain and physical development.
“Disrupted sleep can affect brain development and result in early temperament problems which then leads to a cascade of problems: social, behavioural, academic.”
The study looked at children who were adopted at birth. This eliminated any genetic effect which might affect both the child and the parent such as a predisposition towards being more anxious.
Professor Harold said that while genes did still play a part in a child’s development, this study showed that “the message is that a couple’s exchanges do have an effect on the child”.
Dr Jamie Houston, a consultant paediatrician at Lorn and Islands Hospital in Scotland, said: “Parents need to be aware of the stressors that affect them and minimise the effect on their children.
“There is an increasing body of research around the effect of early life and that the early brain becomes hard wired, forming the basis for the rest of life.
“Sleeping difficulties have been linked with difficulties with behaviour including attention deficit hyperactivity disorder (or ADHD).”
Dr Jon Goldin, consultant child and adolescent psychiatrist at Great Ormond Street Hospital said: “This study supports clinical experience that even young infants are aware of, and sensitive to, the emotional climate at home.
“For lots of children, as with adults, night time is a period when anxieties can particularly surface.
“This study suggests that children who have increased anxiety levels, for example due to exposure to parental marital conflict, are more susceptible to sleep problems and that this difficulty can endure over time.
“Relationship problems and conflict between their parents can have a significant impact on a child’s well-being, sense of security and self-esteem.”