The broadcast channel with confidentialmessages (BCC) models the communication scenario in which a transmitter sends simultaneously common and confidential information to two receivers. The common information must be received by both receivers while the confidential information is designated for one receiver only and must be secured against the other one. The performance of this system is usually characterized by its secrecy capacity region determining the maximum transmission rates. In this chapter, the issue of whether this secrecy capacity region depends continuously on the system parameters or not is examined. In particular, this is done for compound channels, in which the users know only that the true channel realization is constant for the whole duration of transmission and this comes from a pre-specified uncertainty set. The secrecy capacity region of the compound BCC is shown to be robust in the sense that it is a continuous function of the uncertainty set.