The tip shape of a gallium liquid-metal ion/electron emitter has been observed in situ in the Halle 1 MeV electron microscope in both the ion and electron emission modes. In the ion emission mode deviations of the liquid-metal cone shape from the Taylor cone are found. Starting at low emission currents (1_e ≈ 2μA) a jet-like protrusion of the Taylor cone vertex was observed. There was a linear dependence of the decrease of the cone half-angle α and of the increase of the length l of the jet-like protrusion on the increased emission current. The experimental results are in good agreement with the calculations of the jet parameters. Also dynamical effects as e.g. droplet emission and spatial shifts of the Taylor cone are registrated during the experiments. Emission of "Faraday droplets" was observed in the Taylor cone surroundings. The radius of the droplets varied between 0.04 and 0.5 μm. In the electron emission mode, an emitter of a tip radius of 20μm shows behaviour different from that of a tip radius of 0.5μm. In the first case pulse-like electron emission was observed, which starts at the onset voltage of the formation of the Taylor cone. Processes of the formation and disappearance of the Taylor cone had not been observed during these in situ experiments in the HV TEM. In the second case of a sufficiently sharp emitter, electron emission starts below the onset voltage of the formation of the Taylor cone. No stable liquid micro-protuberances were observed in the voltage range between the onset voltages of electron emission and ion emission. If the extraction voltage is increased to attain the value of the onset voltage of the formation of the Taylor cone, an ëxplosive" emission process is observed, which also results in an alteration of the underlying tungsten tip. If the voltage is further increased, pulse-like electron emission without any indication of the formation of a Taylor cone is observed analogously to the first case. Our investigations verify the model established by Rao et al.