It is suggested to use the integral Faddeev equations in the Alt-Grass
berger-Sandhas form to calculate the muon transfer reactions relevant
to muon-catalyzed fusion. Similar equations derived while neglecting t
he electron mass compared to the ion masses, were successfully used fo
r the description of the electron transfer reactions in the ion-atomic
collisions. The corrections due to the finiteness of the muon mass ar
e discussed.