Integrable Kondo impurities in two cases of one-dimensional q-deformed t-J
models are studied by means of the boundary Z(2)-graded quantum inverse sca
ttering method. The boundary K matrices depending on the local magnetic mom
ents of the impurities are presented as nontrivial realizations of the refl
ection equation algebras in an impurity Hilbert space. Furthermore, these m
odels are solved by using the algebraic Bethe ansatz method and the Bethe a
nsatz equations are obtained.