  The notion of local subgroupoid as a generalisation of a local equivalence
relation was defined in a previous paper by the first two authors. Here we use
the notion of star path connectivity for a Lie groupoid to give an important
new class of examples, generalising the local equivalence relation of a
foliation, and develop in this new context basic properties of coherence, due
earlier to Rosenthal in the special case. These results are required for
further applications to holonomy and monodromy.
