Kanban Control Systems are widely used to control the release of parts in multistage manufacturing systems operating under a pull mechanism, i.e. production of new parts is triggered based on the actual demands arriving to the output of the system. Most of the work on Kanban Control Systems deals with single-product manufacturing systems, although Kanban Control Systems have also been used in multiproduct environments. The aim is to study in detail the behaviour of Kanban Control Systems in the context of multiproduct manufacturing systems. In addition to the classical Kanban Control System, we also consider two more general Kanban-Like Control Systems known as Generalized Kanban Control System and Extended Kanban Control System. When extending these pull control mechanisms to multi-product systems, we distinguish two cases, whether kanbans are dedicated to a single part type or shared among the different part types. We provide an in-depth analysis of each of the resulting control mechanism and discuss some important issues arising from the study.