In this paper a new type of digital proxy signature is proposed.The proxy signature allows a designated person, called a proxy signer, to sign on behalf of an original signer.Classification of the proxy signatures is shown from the point of view of the degree of delegation, and conditions of a proposed proxy signature for partial delegation are clarified.The proposed proxy signature scheme is based on the discrete logarithm problem.Compared to the consecutive execution of the ordinary digital signature schemes, it has a direct form, and a verifier does not need a public key of a user other than the original signer in the verification stage.Moreover, it requires less amount of computational work than the consecutive execution of the signature schemes.Due to this efficiency together with the delegation property, an organization, e.g. a software company, can very efficiently create many signatures of its own by delegating its signing operations to multiple employees.Another attractive feature of the proposed schemes is their highapplicability to other ordinary signature schemes based on the discrete logarithm problem.For instance, designated confirmer proxy signatures can be constructed.Furthermore, using a proposed on-line proxy updating protocol, the original signer can revoke proxies of dishonest proxy signers.