This paper addresses a fundamental problem in resource management for flow-based hybrid switching systems. Such systems aim at efficiently transporting layer 3 connectionless IP traffic over layer 2 connection-oriented ATM switching fabrics. One idea behind flow-based hybrid switching is first to decompose individual IP packet streams into flows and then to classify them into short-lived flows and long-lived flows. While the short-lived flows are best forwarded by the embedded software through permanent virtual connections (PVC), the long-lived flows are more effectively transmitted by hardware through to-be-established switched virtual connections (SVC). Clearly the flow classification mechanism will have great impact on the utilization of the system's resources. Unlike the traditional emphasis on resources such as link bandwidth and cell buffer size, our paper focuses on the resources which are directly associated with packet processing power, signaling capacity and routing table size. Our study indicates that the presently available static flow classification methods have a vital shortcoming in balancing the utilization of the system's resources. We propose a novel approach for adaptive flow classification which can balance the utilization of system resources to match the time varying traffic characteristics. After formulating the proposed flow adaptation as a stochastic control problem, a heuristic algorithm is developed. The simulation study based on real traces shows the viability of the proposed flow adaptation for dynamic resource management in flow-based hybrid switching system design.