In this paper we develop a theory for an extended version of the (n/nu)-Sti
llinger cluster that has been used in nucleation theory, where n means the
number of particles constituting the cluster characterized by the volume nu
. The "extended cluster" incorporates some of the surrounding supersaturate
d vapor. This cluster, although requiring more extensive simulation than th
e original (n/nu)-Stillinger cluster, is almost devoid of approximation. It
maintains the non-ad-hoc nature of the original (n/nu)-Stillinger cluster
implicitly. The theory of the cluster is also applicable to clusters which
avoid redundancy by some other means than the so-called "connectivity requi
rement." Simulation of the extended cluster is now being implemented and wi
ll be used in the theory of the homogeneous nucleation rate. [S1063-651X(99
)08307-5].