  The monodromy action in the homology (generally with twisted coefficients) of
complements of stratified complex analytic varieties depending on parameters is
studied. For a wide class of local degenerations of such families (stratified
Morse singularities) local monodromy and variation operators are reduced to
similar operators acting in the transversal slices of corresponding strata. In
particular, these results imply a main part of F. Pham's generalized
Picard--Lefschetz formulae.
