Anonymous proxy signatures are very useful in the construction of anonymous credential systems such as anonymous voting and anonymous authentication protocols. As a basic requirement, we should ensure an honest proxy signer is anonymous. However, in order to prevent the proxy signer from abusing the signing right, we should also allow dishonest signers to be traced. In this paper, we present three novel anonymous proxy signature schemes with different levels of (namely, public, internal and original signer) traceability. We define the formal definitions and security models for these three different settings, and prove the security of our proposed schemes under some standard assumptions.