  We find a one-parameter family of long-lived physical string states in type
II superstring theory. We compute the decay rate by an exact numerical
evaluation of the imaginary part of the one-loop propagator. Remarkably, the
lifetime rapidly increases with the mass. We find a power-law dependence of the
form $T = const. g^{-2} Mass^\alpha$, where the value of $\alpha $ depends on
the parameter characterizing the state. For the most stable state in this
family, one has $\alpha ~= 5$. The dominant decay channel of these massive
string states is by emission of soft massless particles. The quantum states can
be viewed semiclassically as closed strings which cannot break during the
classical evolution.
