Testing and debugging networks is notoriously difficult. Software-Defined Networks (SDNs) complicate this problem since the network is defined by a program, which may contain third-party or home-grown software. The goal of this project is to facilitate network debugging by exploring runtime checking of correctness properties about stateful network behavior, such as the operation of a stateful firewall or connection tracker. Monitoring stateful properties at runtime intrinsically requires maintaining information about packet history, which presents unique challenges compared to traditional monitoring approaches involving flow statistics or analyzing control traffic. Our present work focuses on identifying requirements for checking stateful properties and exploring platforms for extending switches to support monitoring features.