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We present a new model of verifiable certificateless ring signcryption schemes (VCRSS). We argue that it is an important cryptographic primitive for private and anonymous communication. We also propose an efficient VCRSS scheme based on bilinear pairing. In anonymous communications, our scheme allows the message sender to send the message anonymously, while the confidentiality and authenticity of the message are realized at the same time. If necessary, the real sender can prove his/her identity. Since the previous constructions of ring signcryption rely on the identity-based cryptology, key escrow problem is inevitable. We show that in our new scheme, the problem of key escrow is eliminated. We also prove that our scheme is secure in random oracle model.