  We study the irreducible unitary highest weight representations, which are
obtained from free field realizations, of $W$ infinity algebras ($W_{\infty}$,
$W_{1+\infty}$, $W_{\infty}^{1,1}$, $W_{\infty}^M$, $W_{1+\infty}^N$,
$W_{\infty}^{M,N}$) with central charges ($2$, $1$, $3$, $2M$, $N$, $2M+N$).
The characters of these representations are computed. We construct a new
extended superalgebra $W_{\infty}^{M,N}$, whose bosonic sector is
$W_{\infty}^M\oplus W_{1+\infty}^N$. Its representations obtained from a free
field realization with central charge $2M+N$, are classified into two classes:
continuous series and discrete series. For the former there exists a
supersymmetry, but for the latter a supersymmetry exists only for $M=N$.
