A method for transporting Internet Protocols (IP's) over an Asynchronous Transfer Mode (ATM) network that exhibits the strengths of ATM, namely packet interleaving (using cell-based transport) with Quality of Service support for connection-oriented traffic (such as multiclass native ATM traffic and flows-based IP traffic using RSVP), while optimizing the connectionless requirements of existing IP traffic. Advantageously, both the IP protocol stack and ATM protocol stack operate as peers over ATM cell transport hardware. The method exploits an "implicit" signaling/control phase characteristic of IP traffic/protocols thereby minimizing setup. The implicit signaling phase is used to map a flow from a routed path to a switched path immediately upon transmission of a first packet. Similarly, particular packets may be immediately transported over the routed path even after establishment of the switched path. This mapping from the routed path to the switched path and vice versa is based upon the structure/semantics of the protocol driving the flow and not just the duration of the flow as done with prior-art methods. Consequently, while prior-art methods require cell-level counters to monitor activity (or lack thereof) for switching state, the method uses explicit control messages and soft-state at the IP level (as opposed to the cell level) to do the same. Advantageously, the method imposes no switching overhead as there is no coordination between neighboring nodes when a flow is moved from the routed path to the switched path.