In this paper, we propose mapped two-way water filling(MTWF) scheme to maximize energy efficiency(EE) for hybrid bursty services with quality of services(Qo S) requirements in two-way multirelay(TWMR) OFDM networks. The bursty traffic is first analyzed by strictly proved equivalent homogeneous Poisson process, based on which the Qo S requirements are converted into sum-rate constraints. The formulated non-convex EE maximization problem, including subcarrier assignment, relay selection(RS) and rate allocation, is NP-hard involving combinatorial optimization. To conduct optimal RS on each subcarrier without priori bursty traffic knowledge, we utilize some approximate relationships under high data rate demands to remove its dependence on two-way data rates, and simplify the whole optimization problem as well. After the optimal channel configuration is obtained, which only depends on channel conditions, subcarrier assignment is attained through elitist selection genetic algorithm(ESGA), and rate allocation of each service is fulfilled by deducing two-way water filling principle. A new equivalent optimization objective function is proposed next as the simple evaluating index in ESGA to reduce complexity. Finally, simulations are carried out to verify the superiority and convergence of our scheme, as well as the applicability for different scenarios. In this paper, we propose mapped two-way water filling (MTWF) scheme to maximize energy efficiency (EE) for hybrid bursty services with quality of services (Qo S) requirements in two-way multirelay (TWMR) is first analyzed by strictly proved equivalent homogeneous Poisson process, based on which the Qo S requirements are converted into sum-rate constraints. The formulated non-convex EE maximization problem, including subcarrier assignment, relay selection (RS) and rate allocation, is NP To undertake optimal RS on each subcarrier without priori bursty traffic knowledge, we utilize some approximate relationships under high data rate demands to remove its dependence on two-way data rates, and simplify the whole optimization problem as well. After the optimal channel configuration is obtained, which only depends on channel conditions, subcarrier assignment is attained through elitist selection genetic algorithm (ESGA), an d rate allocation of each service is fulfilled by deducing two-way water filling principle. A new equivalent optimization objective function is proposed next as the simple evaluating index in ESGA to reduce complexity. Finally, simulations are carried out to verify the superiority and convergence of our scheme, as well as the applicability for different scenarios.