Non-interactive non-repudiation is a very important property of signcryption which enables a receiver to settle a repudiation dispute with the help of a judge without the need to engage in costly multi-round interactive communications with the judge. In this paper, we construct the generic "Sign-then-Encrypt" and "Encrypt-then-Sign" compositions for signcryption with non-interactive non-repudiation by making use of a normal digital signature primitive as well as a primitive called public key encryption with non-interactive opening. We then analyze the security of both types of compositions.