  Motivated by the dynamic traffic assignment problem, we consider flows over
time model with deterministic queuing. Dynamic equilibria, called Nash flows
over time, have been studied intensively since their introduction by Koch and
Skutella in 2009. Unfortunately, the original model can only handle a single
commodity, i.e., all flow goes from one origin to one destination, therefore,
this theory is not applicable to every-day traffic scenarios. For this reason
we consider Nash flows over time in a setting with multiple commodities, each
with a individual origin and destination. We prove their existence with the
help of multi-commodity thin flows with resetting. This proof gives some
interesting structural insights into the strategy profiles underlying the
equilibria, as they emphasis the inter-commodity dependencies. Finally, we show
that the two special cases of a common origin or a common destination can be
reduced to the single-commodity case.
