  In this paper, we study causal discrete-memoryless relay networks (DMRNs).
The network consists of multiple nodes, each of which can be a source, relay,
and/or destination. In the network, there are two types of relays, i.e., relays
with one sample delay (strictly causal) and relays without delay (causal) whose
transmit signal depends not only on the past received symbols but also on the
current received symbol. For this network, we derive two new cut-set bounds,
one when the causal relays have their own messages and the other when not.
Using examples of a causal vector Gaussian two-way relay channel and a causal
vector Gaussian relay channel, we show that the new cut-set bounds can be
achieved by a simple amplify-and-forward type relaying. Our result for the
causal relay channel strengthens the previously known capacity result for the
same channel by El Gamal, Hassanpour, and Mammen.
