In any string theory there is a hidden, twisted superconformal symmetr
y algebra, part of which is made up by the BRST current and the anti-g
host. We investigate how this algebra can be systematically constructe
d for strings with N - 2 supersymmetries, via quantum Hamiltonian redu
ction of the Lie superalgebras osp(N/2). The motivation is to understa
nd how one could systematically construct generalized string theories
from superalgebras. We also briefly discuss the BRST algebra of the to
pological string, which is a doubly twisted N = 4 superconformal algeb
ra.