A Network Interface device (NI device) coupled to a host computer receives a multi-packet message from a network (for example, the Internet) and DMAs the data portions of the various packets directly into a destination in application memory on the host computer. The address of the destination is determined by supplying a first part of the first packet to an application program such that the application program returns the address of the destination. The address is supplied by the host computer to the NI device so that the NI device can DMA the data portions of the various packets directly into the destination. In some embodiments the NI device is an expansion card added to the host computer, whereas in other embodiments the NI device is a part of the host computer.