Commutative sets of Jucys-Murphy elements for affine braid groups of A ( 1 ) , B ( 1 ) , C ( 1 ) , D ( 1 ) types were defined. Construction of R-matrix representations of the affine braid group of type C ( 1 ) and its distinguished commutative subgroup generated by the C ( 1 ) -type Jucys-Murphy elements are given. We describe a general method to produce flat connections for the two-boundary quantum Knizhnik-Zamolodchikov equations as necessary conditions for Sklyanin's type transfer matrix associated with the two-boundary multicomponent Zamolodchikov algebra to be invariant under the action of the C ( 1 ) -type Jucys-Murphy elements. We specify our general construction to the case of the Birman-Murakami-Wenzl algebras (BMW algebras for short). As an application we suggest a baxterization of the Dunkl-Cherednik elements Y ′ s in the double affine Hecke algebra of type A.