  We study the vanishing cycles on the Milnor fibre of a holomorphic map germ
with special kind of non-isolated singularities which appear in symplectic
geometry. We show, under assumptions given in the text, that the Lefschetz
vanishing cycles freely generate the corresponding homology group of the Milnor
fibre. We study two examples of applications: involutive systems in symplectic
geometry (as characteristic varieties of $\hbar$-differential equations are of
this type) and ajoint orbits in Lie algebras.
