The speed someone walks may predict the likelihood of developing dementia later in life, according to researchers in the US.
They also told a conference that grip strength in middle-age was linked to the chance of a stroke.
The scientists said more studies were needed to understand what was happening.
Experts said the findings raised important questions, but more research was needed.
Suggestions of a link between slow walking speed and poor health have been made before.
A study, published in the British Medical Journal in 2009, said there was a "strong association" between slow walking speed and death from heart attacks and other heart problems. A Journal of the American Medical Association study suggested a link between walking faster over the age of 65 and a longer life.
Dr Erica Camargo, who conducted the latest study at the Boston Medical Centre, said: "While frailty and lower physical performance in elderly people have been associated with an increased risk of dementia, we weren't sure until now how it impacted people of middle age."
Brain scans, walking speed and grip strength were recorded for 2,410 people who were, on average, 62 years old.
Results presented at the Academy of Neurology's annual meeting said that 11 years later, 34 people had developed dementia and 79 had had a stroke.
The researchers said slower walking speeds were linked to a higher risk of dementia and stronger grip with a lower risk of stroke.
Dr Camargo said: "These are basic office tests which can provide insight into risk of dementia and stroke and can be easily performed by a neurologist or general practitioner.
"Further research is needed to understand why this is happening and whether preclinical disease could cause slow walking and decreased strength."
The findings have not yet, however, been published in a peer-reviewed academic journal.
Dr Marie Janson, director of development at Alzheimer's Research UK, said: "Although this study has yet to be published in full, it does raise some important questions about whether physical problems, such as difficulty walking, could precede other symptoms associated with dementia.
"Further study could shed new insight into how walking speed and dementia may be linked."
Dr Anne Corbett, research manager at the Alzheimer's Society, said: "Before people take stock in the strength of a handshake or the speed you cross the road, more research is needed to understand why and what other factors are involved.
"The good news is that there are many things you can do to reduce your risk of developing dementia.
"We recommend you eat a healthy balanced diet, don't smoke, maintain a healthy weight, take regular exercise; and get your blood pressure and cholesterol checked regularly."
The Stroke Association's Dr Sharlin Ahmed, said: "Around a third of those who have a stroke are left with some kind of physical disability, including hand weakness and difficulty walking. However, this is the first time we have seen research that looks at the presence of related symptoms before a stroke.
"This is an interesting study, but a lot more research is needed before we can conclude that strength of grip or walking speed can determine the risk of stroke."