  Matrix Product States can be defined as the family of quantum states that can
be sequentially generated in a one-dimensional system. We introduce a new
family of states which extends this definition to two dimensions. Like in
Matrix Product States, expectation values of few body observables can be
efficiently evaluated and, for the case of translationally invariant systems,
the correlation functions decay exponentially with the distance. We show that
such states are a subclass of Projected Entangled Pair States and investigate
their suitability for approximating the ground states of local Hamiltonians.
