The aim of the thesis was to investigate the importance of physical function for survival in very old people, and furthermore, whether physical exercise could influence physical function, cognitive function, and dependence in activities of daily living (ADLs) in older people with dementia living in nursing homes. The world’s population is ageing. Given the age-related increase in chronic disease such as dementia   and compounded by physical inactivity, the prevalence in need for assistance and are in daily activities in older people is expected to increase in the near future. Gait speed, a measure of physical function, has been shown to be associated with health and survival. However, studies of the  oldest  people  in  the  population,  including  those  dependent  in ADLs,  living  in  nursing  homes  and  with  dementia,  are  few.  Moreover,  in people  with  dementia  physical  exercise  may  improve  physical and  cognitive function and  reduce  dependence  in  ADLs.  Further large studies with high methodological quality and with designs incorporating attention control groups are needed in this population. In addition, no study has compared exercise effects between dementia types. The association between gait speed and survival was investigated in a population based cohort study of 772 people aged 85 years and over. Usual gait speed was assessed over 2.4 metres and mortality followed for five years. Cox proportional hazard regression models adjusted for potential confounders were used in analyses. Effects of physical exercise in people with dementia were investigated in a randomised controlled trial that included 186 participants with various dementia types living in nursing homes. Participants were allocated to the High-Intensity Functional Exercise  (HIFE) program or a seated control activity, which both lasted 45 minutes and held five times  fortnightly for four months. Dependence in ADLs was assessed with Functional Independence Measure and Barthel ADL Index, and balance with Berg Balance Scale. Usual gait speed was evaluated over 4.0 metres in two tests; first using habitual walking aid if any, and thereafter without walking aid and with minimum living support. Global cognitive function was assessed using the Mini-Mental State Examination, the Alzheimer’s Disease Assessment Scale-Cognitive subscale, and   executive function using Verbal fluency. Blinded testers performed assessments at baseline, four (directly after intervention completion) and seven months. Analyses used linear mixed models in agreement with the intention-to-treat principle. Gait speed was found to be an independent predictor of five-year all-cause mortality, where inability to complete the gait test or a gait speed below 0.5 iv meters per second (m/s) was associated with higher mortality risk. In analyses of exercise effects on ADLs there was no difference between groups in the complete sample. Interaction analyses showed a difference in exercise effect according to dementia type at seven months. Positive between-group exercise effects were found for dependence   in ADLs in participants with non-Alzheimer’s type of dementia (non-AD) at four and seven months. In balance, a difference between groups was found at four but not at seven months in the complete  sample, and interaction analyses indicated a difference in effect according to dementia type at four and seven months. Positive between-group exercise effects were found in participants with non-AD.  No difference between groups in gait speed was found in the complete sample, where the majority habitually walked with a walking aid. In interaction analyses exercise effects differed according to walking aid use. Positive between-group exercise effects in gait speed were found in participants that walked unsupported at four and seven months. No difference between groups in cognitive function was found in the complete sample. The effects of exercise on gait speed and cognitive function did not differ according to sex, cognitive level, or dementia type. In conclusion, among people aged 85 or older, including those dependent in ADLs and with dementia, gait speed seems to be a useful clinical indicator of health status. Inability to complete the gait test or a gait speed below 0.5 m/s appears to be associated with higher five-year mortality risk. In older people with mild to moderate dementia living in nursing homes, a four-month high-intensity functional exercise program appeared to attenuate loss of dependence in ADLs and improve balance, albeit only in participants with non-AD type of dementia. Further studies are needed to validate this result. Furthermore, exercise had positive effects on gait speed when tested unsupported, in contrast to when walking aids or minimum support were used. The result implies that the use of walking aids in the gait speed test may conceal exercise effects. The exercise program had no superior effects on global cognition or executive function when compared with an attention control activity. This thesis suggests that, in older people with dementia, exercise effects on physical function rather than cognitive function may explain effects on dependence in ADLs.