  We develop an approach for calculating matrix elements of meson exchange
currents between 3N basis states in (jJ)-coupling and a 3N bound state. The
contribution generated by $\pi$- and $\rho$-exchange are included in the
consideration. The matrix elements are expressed in terms of multiple integrals
in the momentum space. We apply a technique of the partial wave decompositions
and carry out some angular integrations in closed form. Different
representations appropriate for numerical calculations are derived for the
matrix elements of interest. The momentum dependences of the matrix elements
are studied and benchmark results are presented. The approach developed is of
interest for the investigations of deuteron- proton radiative capture and ^3He
photo- and electrodisintegration when the interaction in the initial or final
nuclear states is taken into account by solving the Faddeev equations.
