  The null vectors of an arbitrary highest weight representation of the $WA_2$
algebra are constructed. Using an extension of the enveloping algebra by
allowing complex powers of one of the generators, analysed by Kent for the
Virasoro theory, we generate all the singular vectors indicated by the Kac
determinant. We prove that the singular vectors with given weights are unique
up to normalisation and consider the case when $W_0$ is not diagonalisable
among the singular vectors.
