  It has been shown that there is a sequential embedding structure in a $w_N$\
string theory based on a linearized $W_N$\ algebra. The $w_N$\ string theory is
obtained as a special realization of the $w_{N+1}$\ string. The $w_{\infty}$\
string theory is a universal string theory in this sense. We have also shown
that there is a similar sequence for $N=1$\ string theory. The $N=1\ w_N$\
string can be given as a special case of the $N=1\ w_{N+1}$\ string. In
addition, we show that the $w_3$\ string theory is obtained as a special
realization of the $N=1\ w_3$\ string. We conjecture that the $w_N$\ string can
be obtained as a special $N=1\ w_N$\ string for general $w_N$. If this is the
case, $N=1\ w_{\infty}$\ string theory is more universal since it includes both
$N=0$\ and $N=1$\ $w_N$\ string theories.
