In life insurance mathematics the actuarial equivalence principle is the basic concept to define premiums and premium reserves. The underlying valuation method of this principle is used here on the one hand to generalize equivalence relations of financial mathematics for the continuous-time Markov model for life contingencies and on the other to derive other actuarial equivalence relations for this model. For instance future or past payments due in states of the Markov process are replaced by equivalent insurance benefits payable at the moment of transition from one state to another state.