we identify the linear space spanned by the real-valued excessive functions of a markov process with the set of those functions which are quasimartingales when we compose them with the process. applications to semi-dirichlet forms are given. we provide a unifying result which clarifies the relations between harmonic, co-harmonic, invariant, co-invariant, martingale and co-martingale functions, showing that in the conservative case they are all the same. the talk is based on joint works with iulian cimpean (bucharest) and michael roeckner (bielefeld).