A time-driven block provided in a block diagram model may be executed in an event domain without user modification. The time-driven block is connected to one or more event-driven blocks using event domain signals. The time-driven block automatically adapts to the execution rules of the event domain modeling and simulation environment. The blocks that are configured to execute in more than one modeling and simulation environments are called polymorphic blocks. The polymorphic blocks are identified during the compilation stage of the block diagram model taking into consideration the port and line styles of the blocks. The execution rules of the polymorphic blocks are also determined during the compilation stage of the block diagram model.