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Counterstreaming electron beams drifting along the magnetic field in electron–proton plasmas may lead to the generation of electrostatic (ES) waves and structures widely observed in planetary magnetospheres. In electron–positron plasmas, streaming electron/positron beams along the background magnetic field may first result in ES waves followed by the electromagnetic (EM) waves with substantial magnetic field perturbations, as shown by Jao and Hau [Phys. Rev. E 98, 013203 (2018)]. In this study, we examine the formation of ES and EM waves driven by current free counterstreaming electron beams in electron–ion background plasmas and current free electron–positron beams in electron–proton–positron background plasmas based on one-dimensional EM particle-in-cell simulations with the drift velocity being along the background magnetic field. For the former cases, the effects of ion-to-electron mass ratios are examined, which have implications for two- and three-dimensional particle in cell simulations with reduced mass ratios. For the latter cases, the effects of positrons are examined, which have applications to astrophysical plasma environments and laboratory experiments. It is shown that the presence of positrons or light ions may shorten the occurrence times between the ES and EM waves driven by current free electron beam instability. The EM waves have relatively longer wavelengths as compared to the ES waves and the magnetic field evolution resembles parallel proton firehose instability. The effects of positrons, background compositions, and ion-to-electron mass ratios on the occurrence of ES and EM waves are consistent with the linear fluid theory. [ABSTRACT FROM AUTHOR]