1. A quantitive understanding of the nucleosynthesis process requires the knowledge of the production rates, the masses and the ?-decay characteristics of exotic neutron-rich nu- clei. Nuclear fission is a suitable method of producing such nuclei with masses from 60 - 150. Neutron-rich nuclei close to the r-process path can be produced via photo-fission at the Rossendorf superconducting linear accelerator of high brilliance and low emittance (ELBE) or by means of nuclear reactions at relativistic energies (for example at GSI). If the fission prod- ucts are identified and also their charge numbers are obtained, it will be principally possible to investigate their structure by means of beta-gamma spectroscopy. 2. For the purpose of fission-fragment detection a double time-of-flight (TOF) spectrometer has been developed. The key component of the TOF spectrometer is a TOF detector consisting of multichannel-plate (MCP) detectors with a position-sensitive readout, a foil for secondary electron (SE) production and an electrostatic mirror. The fission fragments are detected by measuring the SEs impinging on the position-sensitive anode after emission from the foil, ac- celeration and deflection by the electrostatic mirror. 3. In the first part of the work, special attention is paid to the relevant methods of building a spectrometer of such type. The functionality of the different detector components is proven in detail. A unique method for the determination of the SE foil thickness with ?-particles is pre- sented. Values for the mirror transmission and scattering are deduced. A dedicated SIMION 3D simulation showed that introducing serpentine like wires with pitch distance of 1 mm is capable of providing transparency of more than 90% without significant impact on the time resolution. 4. Since the performance of the MCP detectors is crucial, optimised schemes for their high- voltage supplies have been implemented successfully. Further enhancement of the setup was achieved by introducing surface-mount device (SMD) elements for signal decoupling, positioned close to the detector surface. Thus, we succeeded in avoiding signal deterioration coming from the additional capacitances and inductivities caused by extra cable lengths. Because the MCP signal decoupling takes place by means of rings with not well-defined impedance, impedance- matching problems arise, causing signal ringing and distortion. An approach towards solving this problem was to build a special fast, wide-band transimpedance amplifier. Using its circuit mounted close to the detectors, a significant reduction of the signal ringing was observed while maintaining the rise time of the detector signal. In order to process the multichannel-plate de- tector signals optimally, a new state-of-the-art constant-fraction discriminator (CFD) based on the amplitude and rise time compensated (ARC) technique with very low threshold capabilities and optimised walk properties has been developed and incorporated into the setup. 5. In our first laboratory test measurements conducted with an ?-particle source, we demonstrated ability of the setup to resolve pattern images placed directly in front of the MCP detector or reflected by the electrostatic mirror. The obtained position resolution for the second case is in the order of 2 mm. We showed that the detection efficiency of the system for ions like He is less than 30 %. This is mainly due to the low number of the electrons liberated from the SE foil. In a setup consisting of two mirror MCP detectors, we could successfully observe the TOF spectrum of a mixed (226Ra, 222Rn, 210Po, 218Po, 214Po) ?-source and found a good agreement with a SRIM simulation. 6. Measurements performed at the FZ Dresden-Rossendorf 5 MV tandem accelerator en- abled us to learn more about the response of the TOF detectors to various beams of heavy ions. The first in-beam experiments clearly showed that the applied setup consisting of two mirror detectors is capable of resolving different 35Cl beam charge states. In a combination with the specially designed wide-band amplifier and dedicated CFDs based on the ARC technique, we managed to achieve an in-beam time resolution of 170 ps per TOF detector. Measurements with ions of Z > 30 resulted in detection efficiencies of greater than 90%. At foil accelerating potentials approximately two times larger than the mirror deflection voltage, most of the SEs gain enough energy to pass through the electrostatic mirror without being deflected towards the MCP surface. Thus, an abrupt drop of the efficiency curve was observed - the “transparent” mode of the mirror. 7. Properties of electrons ejected from thin foils from heavy ions have been also investigated. From the MCP pulse-height-distribution spectra, a number for the forward-emitted SEs ejected by 35Cl beam was deduced. A method for obtaining widths of the SE energy distributions from the drop of the efficiency curve for various ions has been proposed. Assuming that the efficiency curve as a function of the accelerating voltage follows an error function, its standard deviation gives the standard deviation of the SE energy distribution. Another method based on the TOF technique for reconstructing the secondary electron velocity and energy distribution was also invented. It was found that the resulting mean SE velocity closely approaches the one of the beam ions. This phenomenon was attributed to the so-called “convoy” electrons. 8. The obtained position resolution for beams like 35Cl, 79Br and 107Ag at stable detection efficiency was better than 1.8 mm. It was demonstrated that with increasing the foil accelerat- ing voltage, the position resolution improves due to the minimised SE angular spread. Such a mode of operation was favoured until the mirror “semi-transparency” regime was reached, after which increasing further the accelerating potential could lead to a position resolution worsen- ing. An explanation of the fact could be the deterioration of the anode timing signals or some defocusing effects arising from the mirror wires field at high accelerating voltages. 9. Testing photo-fission experiments were performed at the bremsstrahlung facility at the ELBE accelerator. For the first time a spectrometer of this kind was successfully employed for bremsstrahlung-induced photo-fission measurements. The setup consisted of two mirror detectors (first arm) and a 80 mm diameter MCP detector (second arm) with a 238U target positioned in between. TOF measurements with two bremsstrahlung end-point energies of 12.9 and 16.0 MeV were carried out. A clear cut separation of the TOF peaks for the medium- mass and heavy fission fragments was observed. At these experimental test runs, we did not aim at one-by-one fission fragment mass resolution, since this may be the purpose of a more specific experiment utilising a much thinner fissile source than the one applied here (minimum straggling of the fragments inside the target is required) and considerably better statistics. It was possible to estimate the photo-fission production rate for the two measuring cases and to compare the obtained results with data from other measurements.