  We define {\bf primitive derivations} for Coxeter arrangements which may not
be irreducible. Using those derivations, we introduce the {\bf primitive
filtrations} of the module of invariant logarithmic differential forms for an
arbitrary Coxeter arrangement with an arbitrary multiplicity. In particular,
when the Coxeter arrangement is irreducible with a constant multiplicity, the
primitive filtration has already been studied, which generalizes the Hodge
filtration introduced by K. Saito.
