  We show that a family of isolated complete intersection singularities (ICIS)
with constant total Milnor number has no coalescence of singularities. This
extends a well known result of Gabrielov, Lazzeri and L\^e for hypersurfaces.
We use A'Campo's theorem to see that the Lefschetz number of the generic
monodromy of the ICIS is zero when the ICIS is singular. We give a pair
applications for families of functions on ICIS which extend also some known
results for functions on a smooth variety.
