MILNOR FIBRATIONS AND THE THOM PROPERTY FOR MAPS f(g)over-bar

We prove that every map-germ f (g) over bar (C-n, <(0))under bar>->(C, 0) with an isolated critical value at 0 has the Thom a(f (g) over bar)-property. This extends Hironaka's theorem for holomorphic mappings to the case of map-germs f (g) over bar and it implies that every such map-germ has a Milnor-Le fibration defined on a Milnor tube. One thus has a locally trivial fibration empty set : S-epsilon \ K S-1 for every sufficiently small sphere around (0) under bar where K is the link of f (g) over bar and in a neighbourhood of K the projection map Empty set is given by f (g) over bar/vertical bar f (g) over bar vertical bar.