  In a previous paper we described a procedure for computing the renormalized
masses and S-matrix elements in bosonic string theory for a special class of
massive states which do not mix with unphysical states under renormalization.
In this paper we extend this result to general states in bosonic string theory,
and argue that only the squares of renormalized physical masses appear as the
locations of the poles of the S-matrix of other physical states. We also
discuss generalizations to Neveu-Schwarz sector states in heterotic and
superstring theories.
