  In this paper we propose the notion of cluster superalgebras which is a
supersymmetric version of the classical cluster algebras introduced by Fomin
and Zelevinsky. We show that the symplectic-orthogonal supergroup $SpO(2|1)$
admits a cluster superalgebra structure and as a consequence of this, we deduce
that the supercommutative superalgebra generated by all the entries of a
superfrieze is a subalgebra of a cluster superalgebra. We also show that the
coordinate superalgebra of the super Grassmannian $G(2|0; 4|1)$ of chiral
conformal superspace (that is, $(2|0)$ planes inside the superspace $\mathbb
C^{4|1}$) is a quotient of a cluster superalgebra.
