West Africa in general and Burkina Faso in particular are facing climate hazards that are becoming increasingly severe. Periods of drought and a spatiotemporal distribution of rainfall, out of phase with the agricultural calendar, make the already difficult situation more challenging. Thus, the cultivation of varieties resistant to water stress is necessary to sustain production, hence this study aimed at evaluating the physiological, agronomic and biochemical responses of four sesame (Sesamum indicum L.) varieties (S-42, Wollega, 32-15 and Humera) and six descendants of S-42 to continuous water deficit. There were three water supply treatments: watering every other day at soil field capacity was the control; water supply at ¾ soil field capacity (moderate deficit) and water supply at ¼ soil field capacity (severe deficit). A randomised complete block design with 30 treatment combinations (ten accessions and three water supply treatments) was used in the greenhouse. The water deficit, whether moderate or severe, caused a reduction in growth, development and water content. Water deficit caused an increase in the foliar content of total chlorophyll, sodium, potassium and magnesium in all the plants of the varieties and descendants, with a greater effect for the severe deficit. Seed number and weight decreased with the intensity of water deficit in all varieties and lines. Moderate water deficit caused the following rates of reduction in capsule yields: SMK-2 (20.4%), SMK-5 (25.8%), SMK-3 (27.3%), Humera (30.7%), S-42 (32.2%), SMK-4 (35.8%), SMK-1 (36.8%), SMK-6 (38.9%), 32-15 (45.3%) and Wollega (61.0%). Severe deficit caused capsule yield reduction of: SMK-2 (46.3%), SMK-5 (46.4%), SMK-3 (52.7%), Humera (78.2%), S-42 (48.6%), SMK-4 (46.0%), SMK-1 (50.7%), SMK-6 (51.0%), 32-15 (76.6%) and Wollega (84.2%). The variety most affected by the water deficit (moderate or severe) was Wollega. The variety S-42 and all the descendants were the most resistant, especially the descendant SMK-2.