In recursive network architectures such as RINA or RNA, it is natural for multiple layers to carry out congestion control.  These layers can be stacked in arbitrary ways and provide more ways to use feedback than before (which of the many controllers along an end-to-end path should be notified?). This in turn raises concerns regarding stability and performance of such a system of interacting congestion control mechanisms. In this paper, we report on a  first analysis of feedback methods in recursive networks that we carried out using a fluid model with a packet queue approximation. We find that the strict pushback feedback based on queue size can have stability issues, but robust control can be achieved when each congestion controller receives feedback from all sources of congestion within and below its layer.