Despite the fact that extensive research has been done on malaria and HIV/AIDS, they are still major public health problems in Uganda with annual estimates of 10 million cases and 43,000 deaths for malaria and an HIV prevalence of 5.4% that has not changed since 2008. In this thesis, malaria prevalence and the associated risk factors in children below the age of five was investigated. Data from the Uganda Demographic Health Survey were analyzed on 7,336 children. Logistic regression was used to examine the risk factors of malaria. Malaria prevalence decreased with use of bed nets, an increase in the child's wealth status, an increase in the mother's education level and also with an increase in the child's age. Interactions between age and wealth index, and residence and wealth index were significantly associated with malaria prevalence. Prevalence was also higher among rural residents. It is suggested that malaria control measures be targeted to less advantaged groups of people. Knowledge of prevention and transmission of HIV/AIDS among 2,386 adult men and 8,531 adult women in Uganda was also examined in the thesis using the Uganda Demographic Health Survey. Logistic regression was used to examine determinants of knowledge of prevention and transmission of HIV/AIDS. Knowledge was generally higher among the men. Knowledge also increased with increases in wealth status and educational attainment. It is suggested that health education especially among women must underlie intervention programs to influence prevention and transmission of HIV/AIDS in Uganda.