Dynamic spectrum access is an important issue in cognitive radio networks (CRNs) as secondary users (SUs) can benefit from accessing the vacant licensed channels of primary users (PUs). In this paper, we consider the problem of competitive distributed spectrum access in CRNs with quality of service (QoS) constraints. We first propose a distributed matching algorithm (DMA) to handle spectrum access in a QoS-constrained CRN. We then propose a fast distributed matching algorithm (FDMA) for competitive spectrum access in a large- scale CRN. The distributed algorithms for the PU and SU are given separately for practical implementation. The performance and complexity of both algorithms are analyzed and demonstrated via simulation results.