We present a new primitive—Append-only Signatures (AOS)—with the property that any party given an AOS signature Sig[M1] on message M1 can compute Sig[M1 M2] for any message M2, where M1 M2 is the concatenation of M1 and M2. We define the security of AOS, present concrete AOS schemes, and prove their security under standard assumptions. In addition, we find that despite its simple definition, AOS is equivalent to Hierarchical Identity-based Signatures (HIBS) through efficient and security-preserving reductions. Finally, we show direct applications of AOS to problems in network security. Our investigations indicate that AOS is both useful in practical applications and worthy of further study as a cryptographic primitive.