Abstract. The invariants of a mixed two-qubit system are discussed. These are polynomials in the elements of the corresponding density matrix. They are counted by means of group-theoretic branching rules and the Molien function is determined. The fundamental invariants are then explicitly constructed and the relations between them are found in the form of syzygies. In this way, complete sets of primary and secondary invariants are identified: there are 10 of the former and 15 of the latter.

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