  Integrable Kondo impurities in two cases of the one-dimensional $t-J$ model
are studied by means of the boundary ${\bf Z}_2$-graded quantum inverse
scattering method. The boundary $K$ matrices depending on the local magnetic
moments of the impurities are presented as nontrivial realizations of the
reflection equation algebras in an impurity Hilbert space. Furthermore, these
models are solved by using the algebraic Bethe ansatz method and the Bethe
ansatz equations are obtained.
