  The interaction of a Lie algebra $\LL,$ having a weight space decomposition
with respect to a nonzero toral subalgebra, with its corresponding root system
forms a powerful tool in the study of the structure of $\LL.$ This, in
particular, suggests a systematic study of the root system apart from its
connection with the Lie algebra. Although there have been a lot of researches
in this regard on Lie algebra level, such an approach has not been considered
on Lie superalgebra level. In this work, we introduce and study extended affine
root supersystems which are a generalization of both affine reflection systems
and locally finite root supersystems. Extended affine root supersystems appear
as the root systems of the super version of extended affine Lie algebras and
invariant affine reflection algebras including affine Lie superalgebras. This
work provides a framework to study the structure of this kind of Lie
superalgebras refereed to as extended affine Lie superalgebras.
