  We study associative graded algebras which have a ``complete flag'' of cyclic
modules with linear free resolutions, i.e., algebras over which there is a
cyclic Koszul module with every admissible number of relations (from zero up to
the number of generators of the algebra). Commutative algebras with the same
property has been studied in several papers by A. Conca and others. Here we
present a non-commutative version.
  We introduce the concept of Koszul filtration in non-commutative algebras and
study its connections with Koszul algebras and algebras with quadratic Groebner
bases. Also, here are considered several examples, such as ``Groebner flags'',
generic algebras, and algebras with one relation. A generalization of the
concept Koszul filtration (generalized Koszul, or rate, filtration) leads to
algebras with finite Backelin's rate and to coherent algebras. One of our main
results is that every algebra with Koszul filtration (or with finite rate
filtration) has rational Hilbert series.
