Conditional independence structures, often called graphical models, play a central role in the statistical analysis of complex systems. The talk identifies a subclass of these, consisting of hierarchical marginal log-linear models. Such models are smooth, which implies the applicability of standard asymptotic theory and also simplifies interpretation. Further, a hierarchical marginal log-linear parameterization and minimal specification of the models is given, implying the number of degrees of freedom and the applicability of standard methods to compute maximum likelihood estimates. The results are applied to Markov models associated with chain graphs, yielding smoothness results. The parameterization obtained may be used to define and interpret path models for chain graphs. The talk is based on a joint paper with W. Bergsma and R. Nemeth, to appear in Biometrika.