In this paper, we address the dynamics associated with living-arrangement decisions of sick, elderly individuals. Using data from the Panel Study of Income Dynamics and its Parental Health Supplement, we construct the complete living-arrangement histories of elderly individuals in need of care. We use a simultaneous random-effects competing-risks model to analyze the impact of demographic characteristics, health and wealth on the living-arrangement decisions of sick elderly individuals while taking into account state and duration dependence as well as unobserved heterogeneity. We find that state and duration dependence serve as important predictors for the living arrangement choices of sick elderly individuals.