  We consider the tree-level scattering amplitudes in the NS-NS (Neveu-Schwarz)
massless sector of closed superstrings in the case where one external state
becomes soft. We compute the amplitudes generically for any number of
dimensions and any number and kind of the massless closed states through the
subsubleading order in the soft expansion. We show that, when the soft state is
a graviton or a dilaton, the full result can be expressed as a soft theorem
factorizing the amplitude in a soft and a hard part. This behavior is similar
to what has previously been observed in field theory and in the bosonic string.
Differently from the bosonic string, the supersymmetric soft theorem for the
graviton has no string corrections at subsubleading order. The dilaton soft
theorem, on the other hand, is found to be universally free of string
corrections in any string theory.
