It's a slight alteration of the "Successors of Selected Nodes" in the Select Elements dialog box. Only those successors will be selected who don't have any unselected predecessors.
This is useful if the nodes represent a flow chart where each step cannot begin until all its predecessors have been completed. Selection of the node represents completion of a that step. Thus, by repeating the same proposed "Nodes with all predecessors selected" command, one can see how a flow chart progresses.
Thank you very much! (Perhaps there is already another way to accomplish this?)