We consider the canonical structure of the Green-Schwarz superstring in 9+1 dimensions using the Dirac constraint formalism; it is shown that its
structure is similar to that of the superparticle in 2+1 and 3+1
dimensions. A key feature of this structure is that the primary Fermionic
constraints can be divided into two groups using field-independent projection
operators; if one of these groups is eliminated through use of a Dirac Bracket
(DB) then the second group of primary Fermionic constraints becomes first
class. (This is what also happens with the superparticle action.) These primary
Fermionic first class constraints can be used to find the generator of a local
Fermionic gauge symmetry of the action. We also consider the superstring action
in other dimensions of space-time to see if the Fermionic gauge symmetry can be
made simpler than it is in 2+1, 3+1 and 9+1 dimensions. With a 3+3 dimensional target space, we find that such a simplification occurs. We
finally show how in five dimensions there is no first class Fermionic
constraint.Comment: 24 pages, Latex2e; further comments and clarifications adde