  The mechanisms of nuclear transfer reactions are described for the transfer
of two nucleons from one nucleus to another. Two-nucleon overlap functions are
defined in various coordinate systems, and their transformation coefficients
given between coordinate systems. Post and prior couplings are defined for
sequential transfer mechanisms, and it is demonstrated that the combination of
`prior-post' couplings avoids non-orthogonality terms, but does not avoid
couplings that do not have good zero-range approximations. The simultaneous and
sequential mechanisms are demonstrated for the $^{124}$Sn(p,t)$^{122}$Sn
reaction at 25 MeV using shell-model overlap functions. The interference
between the various simultaneous and sequential amplitudes is shown.
