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The Large Hadron Collider (LHC) currently in operation intends to explore particle physics on the TeV scale. The International Linear Collider (ILC) and the Compact Linear Collider (CLIC) are being designed to measure the properties of particles possibly discovered at the LHC with high precision. Very forward detector systems at these machines are needed for the precise measurement of the luminosity and to approach full polar angle coverage. In the current detector concepts for linear collider detectors two electromagnetic calorimeters, Beam Calorimeter (BeamCal) and Luminosity Calorimeter (LumiCal), are foreseen. Both calorimeters are designed as sandwich calorimeters with tungsten absorber layers instrumented with finely segmented sensors. Due to a large amount of beamstrahlung remnants hitting BeamCal at the innermost radii, the sensors must withstand up to 1 MGy radiation dose per year. In this thesis two types of sensor materials were investigated: single crystal chemical vapour deposition diamonds (scCVDD) and gallium arsenide doped by chromium (GaAs:Cr). The very forward calorimeters ensure coverage for high energy electrons, positrons and photons down to very low polar angles. Within this thesis, simulation studies are presented for different beam parameters of the ILC. A new sensor segmentation was proposed to achieve better reconstruction efficiency of single high-energy electrons, positrons and photons on top of the beamstrahlung background. Only for a few years ago polycrystalline diamond sensors have been used for beam diagnostics in high-energy physics experiments. The Compact Muon Solenoid experiment, CMS, at the LHC is instrumented with several detectors for the Beam Conditions and Radiation Monitoring. The Fast Beam Conditions Monitor (BCM1F) is part of these systems. Here for the first time single crystal diamond sensors have been used. Eight detectors, comprising each a single crystal sensor and front-end electronics, are positioned around the beam pipe on both sides of the interaction region. They monitor the beam halo to protect the inner CMS detectors from adverse beam conditions and ensure high quality data for CMS. In this thesis, BCM1F data is evaluated for intrinsic time resolution and performance under harsh radiation conditions. Furthermore, it is investigated if it can be used for a bunch by bunch on-line luminosity measurement. The second type of sensor, made of GaAs:Cr, was produced in Tomsk State University and tested as a candidate for the BeamCal for future ILC and CLIC detectors. Several GaAs:Cr sensors were characterized in the laboratory for leakage current and capacitances and used for test beam investigations. Two sensors were assembled with a fan-out, front-end and ADC ASICs to build a fully functional prototype of a sensor plane. Several test beam campaigns were done to measure the performance of the system.