Network traffic statistics show that, because shorter packets predominate in many applications, headers impose a considerable overhead. But the header content is largely repetitive, thus in the past 15 years many packet header compression techniques have been proposed and studied. Header compression is based on differential methods, which introduces error propagation and leads to problems, e.g., in wireless links. This work presents error-resilient header compression by using forward error correction (FEC), which can significantly improve the throughput of header compression in both uni-directional and bi-directional links. The proposed methods are versatile and can work with pre-existing header compression schemes. Simulations demonstrate the advantages of the proposed system in terms of packet loss rates, throughput and delay.