  We introduce a class of commutative superalgebras generalizing cluster
algebras. A cluster superalgebra is defined by a hypergraph called an "extended
quiver", and transformations called mutations. We prove the super analog of the
"Laurent phenomenon", i.e., that all elements of a given cluster superalgebra
are Laurent polynomials in the initial variables, and find an invariant
presymplectic form. Examples of cluster superalgebras are provided by
superanalogs of Coxeter's frieze patterns. We apply the Laurent phenomenon to
construct a new integer sequence extending the Somos-$4$ sequence.
