In the past few years, many excellent studies on proxy signature schemes have been published. Yet, traditional proxy signature schemes are mainly aimed at dealing with one or two separate proxy conditions each. In this article, the authors shall present a generalized version of the (t1/n1–t2/n2) proxy signature scheme based on the discrete logarithms that can be applied to every proxy situation. The (t1/n1–t2/n2) proxy signature scheme allows the original group of original signers to delegate their signing capability to a designated proxy group. The proxy group of proxy signers can cooperatively generate the proxy signature on behalf of the original group. Any verifier can verify the proxy signature on the message with the knowledge of the identities of the actual original signers and the actual proxy signers. Furthermore, some possible attacks have been considered, and our security analysis shows that none of them can successfully break the proposed scheme.