An interface apparatus having a first and a second buffer storage unit, the first buffer storage unit being associated with a first domain and the second buffer storage unit being associated with a second domain, and the buffer storage units being connected to one another for transmitting data. Each of the storage units is of two-stage design and respectively has a first and a second memory, the first and second buffer storage units are connected by unit of connections between the second memory in one buffer storage unit and the first memory in the other buffer storage unit, and data from one domain being written to the first memory and then to the second memory when a transmission operation is no longer pending between the domains.