  In 1933, van Kampen described the fundamental groups of the complements of
plane complex projective algebraic curves. Recently, Ch\'eniot-Libgober proved
an analogue of this result for higher homotopy groups of the complements of
complex projective hypersurfaces with isolated singularities. Their description
is in terms of some "homotopical variation operators". We generalize here the
notion of "homotopical variation" to (singular) quasi-projective varieties.
This is a first step for further generalizations of van Kampen's theorem. A
conjecture, with a first approach, is stated in the special case of
non-singular quasi-projective varieties.
