1. A method of flow control in a network communications device, said network communications device receiving packets, comprising: enqueuing said packets in one or more packet queue structures of said network communications device; scheduling, in said network communications device, said packets for dequeuing from said one or more packet queue structures according to a packet hierarchy; dequeuing said packets, in said network communications device; segmenting, in said network communications device, each said dequeued packet into one or more ATM cells; enqueuing said ATM cells into one or more cell queue structures of said network communications device; scheduling, in said network communications device, said ATM cells for dequeuing from said one or more cell queue structures according to said packet hierarchy; and transmitting said ATM cells through an ATM interface of said network communications device; wherein: said dequeuing said packets is controlled by the presence or absence of one or more feedback signals from said cell queue structures; said scheduling said ATM cells for dequeuing from said one or more cell queue structures employs a first in, first-out buffer; and dequeuing said packets includes: determining which packet queue structures contain a packet ready for dequeuing; determining which virtual circuits of a plurality of virtual circuits, each virtual circuit being associated with one cell queue structure and with a plurality of packet queue structures, have available capacity with reference to a feedback signal from the cell queue structure associated with the virtual circuit; and causing to be dequeued a packet from a packet queue structure associated with a virtual circuit having available capacity and having a highest virtual circuit priority, the particular packet queue structure being the packet queue structure containing a packet ready for dequeuing having the highest priority, as assigned by a Quality of Service policy function.