We present the XDI Model for specifying delay-insensitive circuits, that is, reactive systems that correctly exchange signals with their environment in spite of unknown delays incurred by the interface. XDI specifications capture restrictions on the communication between circuit and environment, treating both parties equally. They can be visualized as state graphs where each arrow is labeled by a communication terminal and each state by a safety/progress label. We investigate various properties that can be extracted from XDI specifications: automorphisms, environment partitions, autocomparison matrix, and classifications of choice, order dependence, and nondeterminism. We introduce a distinction between static and dynamic output nondeterminism, capturing the difference between design freedom and arbitration.