  The superalgebra $\hat{K}'(4)$ and the exceptional N = 6 superconformal
algebra have ``small'' irreducible representations in the superspaces $V^{\mu}
= t^{\mu}\C[t, t^{-1}]\otimes\Lambda(N)$, where N = 2 and 3, respectively. For
${\mu \in \C\backslash \Z}$ they are associated to the embeddings of these
superalgebras into the Lie superalgebras of pseudodifferential symbols on the
supercircle S^{1|N}. In this work we describe $\hat{K}'(4)$ and the exceptional
N = 6 superconformal algebra in terms of matrices over a Weyl algebra.
Correspondingly, we obtain realizations of their representations in $V^{\mu}$
for $\mu = 0$.
