  We consider two examples of solutions of the equations of motion of scalar
field theories with higher derivatives. These are the cosmology of the rolling
tachyon and static spherically symmetric solutions of the scalar field in flat
space. By requiring that the field equations always be hyperbolic and that the
speed of propagation of the small fluctuations are not superluminal, we find
constraints on the form of the allowed interactions in the first case and on
the choice of boundary conditions in the latter. For the rolling tachyon we
find a general class of models which have the property that at large times the
tachyon matter behaves essentially like a non-relativistic gas of dust. For the
spherically symmetric solutions we show how causality influences the choice of
boundary conditions and those which are finite at the origin are shown to have
negative energy density there.
