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One of the key elements in building a time-division- multiplexed (TDM) switch is the time slot interchange (TSI). Given the current optical switching and buffer technologies, TSI-based TDM architectures have many implementation drawbacks, including severe signal attenuation. Some studies showed that some space-time equivalence diagrams can be converted into a delay-unit-based (TSI-free) TDM. This type of architecture is attractive for optical TDM switches, but the techniques discussed in those studies are for rearrangeable switches. Many applications require nonblocking switches where adding a new connection (or a flow) will not cause rearrangement of existing connections. In this paper, we present the design principle for building strictly nonblocking delay-unit-based (TSI-free) optical TDM switches.