  The investigation asymptotic limits on associated data mainly focused on
limit theorems of summands of associated data and on the related invariance
principles. In a series of papers, we are going to set the general frame of the
theory by considering an arbitrary infinitely decomposable (divisible) limit
law for summands and study the associated functional laws converging to L\'evy
processes. The asymptotic frame of Newman (1980) is still used as a main tool.
Detailed results are given when $G$ is a Gaussian law (as confirmation of known
results) and when $G$ is a Poisson law. In the later case, classical results
for independent and identically distributed data are extended to stationary and
non-stationary associated data.
