  We consider two non-relativistic strings and their Galilean symmetries. These
strings are obtained as the two possible non-relativistic (NR) limits of a
relativistic string. One of them is non-vibrating and represents a continuum of
non-relativistic massless particles, and the other one is a non-relativistic
vibrating string.
  For both cases we write the generator of the most general point
transformation and impose the condition of Noether symmetry. As a result we
obtain two sets of non-relativistic Killing equations for the vector fields
that generate the symmetry transformations. Solving these equations shows that
NR strings exhibit two extended, infinite dimensional space-time symmetries
which contain, as a subset, the Galilean symmetries. For each case, we compute
the associated conserved charges and discuss the existence of non-central
extensions.
