The sand bed portion of the Fly River system in Papua New Guinea was influenced significantly by postglacial sea level rise, but this response differed along the three main low-gradient branches of the system: the main stem lower Fly River and its two tributary reaches, the middle Fly River and the Strickland River. A numerical model for valley development over ∼1000 to ∼10,000 year timescales is presented that can account for the coupled morphodynamic evolution of the main stem and its two tributaries. It is shown that the underlying theory includes both advective and diffusive terms for morphodynamic evolution, in contrast to other purely diffusive models for valley development. The advective terms arise due to the inclusion of backwater in the theory. The model is applied to the Fly River system over the 20,000 years since glacial low stand of sea level. Results imply that the relatively low sediment supply to the middle Fly River compared with that to the Strickland probably prevented the middle Fly from keeping pace with aggradation along the downstream lower Fly River. The middle Fly may still be responding to this forcing. It appears unlikely that the middle Fly River was incised more than ∼10 m prior to the onset of base level rise. This implies that the low-stand lower Fly River passed through a zone characterized by channel slopes much steeper than the present slope somewhere between the junction with the Strickland River and the low-stand delta.