  We describe a period map for those simply connected Enriques surfaces in
characteristic 2 whose canonical double cover is K3. The moduli stack for these
surfaces has a Deligne-Mumford quotient that is an open substack of a $\mathbb
P^1$-bundle over the period space. We also give some general results relating
local and global moduli for algebraic varieties and describe the difference in
their dimensions in terms of the failure of the automorphism group scheme to be
reduced.
