The entropy analysis of nonlinear dynamical systems has shown to be fruitful for establishing concepts important in the fields of modern chaos theory. Processes relevant for many pratical sciences appear to occur near the border between order and chaos. Their special features are reflected by a series of block entropies. Some interesting systems show a long memory caused by long range correlations. A more general view on mechanisms creating long range correlations is valuable for a modelling of such systems. I aim to investigate the relation between different mechanisms (1-d maps, coupled maps, grammars) giving rise to slowly decaying memory (power law decay of conditional entropies). The main task is to calculate the profile of conditional entropies. Analytical investigations will involve probabilistic concepts and combinatorial reasoning. Numerical studies will be performed by simulations.