Delegation of rights is a common practice in the real world. Proxy signature schemes have been invented to delegate signing capability efficiently and transparently. In this paper, we present a new nonrepudiable proxy signature scheme. Nonrepudiation means the signature signers, both original and proxy signers, cannot falsely deny later that he generated a signature. In practice, it is important and, sometimes, necessary to have the ability to know who is the actual signer of a proxy signature for internal auditing purpose or when there is abuse of signing capability. The new nonrepudiable proxy signature scheme also has other desirable properties, such as proxy signature key generation and updating using insecure channels. We also show how to construct threshold proxy signature schemes with an example. Threshold signatures are motivated both by the need that arises in some organizations to have a group of employees agree on a given message (or a document) before signing it, as well as by the need to protect signature keys from the attack of internal and external adversaries. Our approach can also be applied to other ElGamal-like proxy signature schemes.