  In this article we are interested in morphisms without slope for mixed Hodge
modules. We first show the commutativity of iterated nearby cycles and
vanishing cycles applied to a mixed Hodge module in the case of a morphism
without slope. Then we define the notion "strictly without slope" for a mixed
Hodge module and we show the preservation of this condition under the direct
image by a proper morphism. As an application we prove the compatibility of the
Hodge filtration and Kashiwara-Malgrange filtrations for some pure Hodge
modules with support an hypersurface with quasi-ordinary singularities.
