In this paper, we study the observability properties of
nonlinear discrete
time systems. Two types of contributions are given. First, we present
observability
criteria in terms of appropriate codistributions.
For particular, but significant, classes of systems
we provide criteria that require only
a finite number of computations. Then, we consider invertible systems
(which includes
discrete-time models obtained by sampling of continuous-time systems)
and prove that the weaker notion of forward-backward
observability is equivalent to
the stronger notion
of (forward) observability.