  The purpose of this contribution is to review some aspects of the loop space
formulation of pure gauge theories having the connection defined over a Lie
algebra. The emphasis is focused on the discussion of the Mandelstam
identities, which provide the basic constraints upon both the classical and the
quantum degrees of freedom of the theory. In the case where the connection is
extended to be valued on a super Lie algebra, some new results are presented
which can be considered as first steps towards the construction of the
Mandelstam identities in this situation, which encompasses such interesting
cases as supergravity in $3+1$ dimensions together with $2+1$ super
Chern-Simons theories, for example. Also, these ideas could be useful in the
loop space formulation of fully supersymmetric theories.
