  We constructed the analytic Milnor fiber is a non-archimedean model of the
classical topological Milnor fibration. In the present paper, we describe the
homotopy type of the analytic Milnor fiber in terms of a strictly semi-stable
model, and we show that its singular cohomology coincides with the weight zero
part of the mixed Hodge structure on the nearby cohomology. We give a similar
expression for Denef and Loeser's motivic Milnor fiber in terms of a strictly
semi-stable model.
