The use of broad consent for genomics research raises important ethical questions for the conduct of genomics research, including relating to its acceptability to research participants and comprehension of difficult scientific concepts. To explore these and other challenges, we conducted a study using qualitative methods with participants enrolled in an H3Africa Rheumatic Heart Disease genomics study (the RHDGen network) in Zambia to explore their views on broad consent, sample and data sharing and secondary use. In-depth interviews were conducted with RHDGen participants (n = 18), study staff (n = 5) and with individuals who refused to participate (n = 3). In general, broad consent was seen to be reasonable if reasons for storing the samples for future research use were disclosed. Some felt that broad consent should be restricted by specifying planned future studies and that secondary research should ideally relate to original disease for which samples were collected. A few participants felt that broad consent would delay the return of research results to participants. This study echoes findings in other similar studies in other parts of the continent that suggested that broad consent could be an acceptable consent model in Africa if careful thought is given to restrictions on re-use.