  We propose a series of new subalgebras of the $W_{1+\infty}$ algebra
parametrized by polynomials $p(w)$, and study their quasifinite
representations. We also investigate the relation between such subalgebras and
the $\hat{\mbox{gl}}(\infty)$ algebra. As an example, we investigate the $\Win$
algebra which corresponds to the case $p(w)=w$, presenting its free field
realizations and Kac determinants at lower levels.
