  Let f be a Z/2Z-spin structureon a closed surface S of genus g>3. We
determine a generating set of the stabilizer of f in the mapping class group of
S consisting of Dehn twists about an explicit collection of 2g+1 curves in S.
If g=3 then we also determine a generating set of the stabilizer of an odd
Z/2Z-spin structure consisting of Dehn twists about a collection of 6 curves.
