  Recent studies have shown that secular evolution of triple systems can play a
major role in the evolution and interaction of their inner binaries. Very few
studies explored the stellar evolution of triple systems, and in particular the
mass loss phase of the evolving stellar components. Here we study the dynamical
secular evolution of hierarchical triple systems undergoing mass loss. We use
the secular evolution equations and include the effects of mass-loss and
mass-transfer, as well as general relativistic effects. We present various
evolutionary channels taking place in such evolving triples, and discuss both
the effects of mass-loss and mass-transfer in the inner binary system, as well
as the effects of mass-loss/transfer from an outer third companion. We discuss
several distinct types/regimes of triple secular evolution, where the specific
behavior of a triple system can sensitively depend on its hierarchy and the
relative importance of classical and general relativistic effects. We show that
the orbital changes due to mass-loss and/or mass-transfer processes can
effectively transfer a triple system from one dynamical regime to another. In
particular, mass loss/transfer can both induce and quench high amplitude
(Lidov-Kozai) variations in the eccentricity and inclination of the inner
binaries of evolving triples. They can also change the system dynamics from an
orderly periodic behavior to a chaotic one, and vice versa.
