This paper studies three existing technical solutions for a self-sovereign identity on blockchains and analyzes the arising issues related to the General Data Protection Regulation (GDPR) of the European Union (EU). In particular, the paper provides an overview of the existing Sovrin self-sovereign identity on the Hyperledger Indy public permissioned blockchain as well as uPort and Jolocom on the Ethereum public permissionless blockchain. The paper then concludes with a discussion on the GDPR-compliance of the blockchain-based identity concepts.