The representation-independent biquadratic identities which Pauli has proved to hold between a Dirac wave function and its adjoint are shown to be generalizable in several ways. To obtain these generalizations it is first shown how the symmetrical Kronecker product of two spinor representations of the orthogonal group in n dimensions decomposes. Then a method is given to express the tensors formed in a particular way from two covariant and two contravariant spinors in terms of those formed in any other way. These results are applied to write explicitly all biquadratic scalar and pseudoscalar identities in 2ν dimensions and all scalar identities in 2ν+1 dimensions. The way to obtain more general tensor identities is indicated.