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We find a one-parameter family of long-lived physical string states in typeII superstring theory. We compute the decay rate by an exact numericalevaluation of the imaginary part of the one-loop propagator. Remarkably, thelifetime rapidly increases with the mass. We find a power-law dependence of theform $T = const. g^{-2} Mass^\alpha$, where the value of $\alpha $ depends onthe parameter characterizing the state. For the most stable state in thisfamily, one has $\alpha ~= 5$. The dominant decay channel of these massivestring states is by emission of soft massless particles. The quantum states canbe viewed semiclassically as closed strings which cannot break during theclassical evolution.Comment: Latex, 5 figures, 35 pages (= 23 pages + appendices). Minor  correction

Decay of long-lived massive closed superstring states: exact results