The problem if and how the so-called Markov properties of a system of linear structural equations for Gaussian variables can be read off the path diagram of the system was discussed by many authors for the case of recursive systems. The issue concerns the compatibility of two different methods of portraying the relationships between variables by means of a diagram or graph, that is, of defining the mathematical meaning of the pictorial object. On the one hand there is the interpretation in linear structural equation modelling of a path diagram as a causal model, where each endogenous variable is associated with a linear equation specifying how this variable depends on the other variables of the model. On the other hand there is the more recent graphical modelling approach in which topographical properties of graphs are used to represent the Markov properties among the variables, i.e. their probabilistic (in)dependencies. There are important differences between the two interpretations of graphical objects. These differences seem substantial and therefore one cannot expect beforehand that, in case of linear structural equation models (LSEM) for Gaussian variables, the two ways of inferring relationships between the variables from the path diagram are consistent. It is known, however, that, provided certain additional conditions are satisfied, the path diagram of a recursive LSEM can be given a consistent interpretation as a graphical model. It can be shown that this is also true for the path diagram of a recursive nonlinear structural equation model (see Pearl, 1995). Pearl’s \(d\)-separation concept and the ensuing Markov property are applied to graphs which may have, between each two different vertices \(i\) and \(j,\) any subset of \(\{i\rightarrow j, i\leftarrow j, i\leftrightarrow j\}\) as edges. The class of graphs so obtained is closed under marginalization. Furthermore, the approach permits a direct proof of the following theorem: The distribution of a multivariate normal random vector satisfying a system of linear simultaneous equations is Markov w.r.t. the path diagram of the linear system.