While a nascent body of research investigates the shift in sub-Saharan Africa's (SSA's) disease burden towards non-communicable diseases (NCDs), very few studies have investigated mental health, specifically depression and anxiety (DA), in SSA. Using the 2012--13 Malawi Longitudinal Study of Families and Health (MLSFH), this paper provides a first picture of the demography of DA among mature adults (= persons aged 45+) in a low-income high HIV-prevalence context. DA are more frequent among women than men, and individuals are often affected by both. DA are associated with adverse outcomes, such as less nutrition intake and reduced work efforts. DA also increase substantially with age for both females and males, and mature adults can expect to spend a substantial fraction of their remaining life time---for instance, 52% for a 55 year old woman---affected by DA. The positive age-gradients of DA are not due to cohort effects, and they are in sharp contrast to the age pattern of mental health that have been shown in high-income contexts where older individuals often experience lower levels of DA and better subjective well-being than middle-aged individuals. While socioeconomic and risk/uncertainty-related stressors are strongly associated with DA, they do not explain the positive age gradients and gender gap in DA. Stressors related to physical health, however, do. Hence, our analyses suggest that the general decline of physical strength and health with age, as is indicated by hand grip strength, and the interference of poor physical health with daily activities, are key drivers of the rise of DA with age among mature adults.