  We give a complete picture of the interaction between Koszul and Ringel
dualities for quasi-hereditary algebras admitting linear tilting
(co)resolutions of standard and costandard modules. We show that such algebras
are Koszul, that the class of these algebras is closed with respect to both
dualities and that on this class these two dualities commute. All arguments
reduce to short computations in the bounded derived category of graded modules.
