Abstract. For a fixed right process X we investigate those functions u for which u(X) is a quasimartingale. We prove that u(X) is a quasimartingale if and only if u is the difference of two finite excessive functions. In particular, we show that the quasimartingale nature of u is preserved under killing, time change, or Bochner subordination. The study relies on an analytic reformulation of the quasimartingale property for u(X) in terms of a certain variation of u with respect to the transition function of the process. We provide sufficient conditions under which u(X) is a quasimartingale, and finally, we extend to the case of semi-Dirichlet forms a semimartingale characterization of such functionals for symmetric Markov processes, due to Fukushima.