An essential functionality for context-aware networks would be the ability to classify traffic into logical flows and to determine the characteristics of these flows, for various purposes such as QoS provisioning, traffic limiting and shaping, security filtering and access control, policy-based routing, adaptation, service triggering, and long-term network monitoring and management. In this paper we explore a multi-dimensional scheme of classifying flows based on both their intrinsic characteristics and on some relevant external factors, that is, we classify flows based on their context. We demonstrate the use of ontologies to formally model flow context for software design purposes and as a vocabulary for runtime context exchange and processing, and describe the implementation of a system that demonstrates contextbased flow classification.