  A novel Lie-superalgebraic description of the superstring in the
super-Minkowskian background is extracted from the Cartan-Eilenberg
super-1-gerbe geometrising the higher gauge field (the Green-Schwarz
super-3-cocycle) that couples to the supercharge carried by the superstring.
The description assumes the form of a hierarchy of Lie superalgebras integrable
to a hierarchy of Lie supergroups and provides a manifestly supersymmetric
model of a family of supermanifolds defining a trivialisation of the
super-1-gerbe over the embedded superstring worldsheet. The trivialisation,
obtained in a purely topological formulation of the superstring dynamics dual
to the standard Nambu-Goto-type one, conforms with the gerbe-theoretic
representation of extended sources of higher gauge fields known from previous
studies of the $\sigma$-model of the bosonic string.
