Families of semipermeable curves in differential games with the homicidal chauffeur dynamics are studied both from theoretical and computational points of view. The knowledge of such families is very useful because semipermeable curves bound capture sets in games of kind. They can also appear as barrier lines on which value functions of time-optimal differential games are discontinuous. Two examples of differential games with the homicidal chauffeur dynamics are considered. Capture sets are constructed using semipermeable curves. The results are verified through computation of level sets of the value functions in the related time-optimal games. (C) 2004 Elsevier Ltd. All rights reserved.