  We give a complete picture of the interaction between Koszul and Ringel
dualities for graded standardly stratified algebras (in the sense of Cline,
Parshall and Scott) admitting linear tilting (co)resolutions of standard and
proper costandard modules. We single out a certain class of graded standardly
stratified algebras imposing the condition that standard filtrations of
projective modules are finite, and develop the tilting theory for such
algebras. Under the assumption of existence of linear tilting (co)resolutions
we show that algebras from this class are Koszul, that both Ringel and Koszul
duals belong to the class, and that these two dualities on this class commute.
