  We discuss one of the generic spacetime consequences of having (1,0)
worldsheet supersymmetry in tachyon-free string theory, namely the appearance
of a ``misaligned supersymmetry'' in the corresponding spacetime spectrum.
Misaligned supersymmetry is a universal property of (1,0) string vacua which
describes how the arrangement of bosonic and fermionic states at all string
energy levels conspires to preserve finite string amplitudes, even in the
absence of full spacetime supersymmetry. Misaligned supersymmetry also
constrains the degree to which spacetime supersymmetry can be broken without
breaking modular invariance, and is responsible for the vanishing of various
mass supertraces evaluated over the infinite string spectrum.
  [Talk delivered at Strings '95, based on material drawn from hep-th/9402006
and hep-th/9409114. To appear in Proceedings.]
