Alfvén/ion-cyclotron waves are important normal modes in a plasma. Their existence can explain several observed features in space plasmas such as temperature anisotropies and preferred heating of certain ion species in the solar corona and the solar wind. The properties of this wave mode and different aspects of the spectral transfer of wave energy in wavenumber space are analyzed. Every plasma wave is a complex interplay between the electromagnetic fields and the plasma particles. The way

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... n/ion-cyclotron waves shape a particle distribution function is treated with kinetic methods in an analytical model, and an additional observational effect in particle measurements is found. The nature of the important Alfvén/ion-cyclotron mode is discussed in a multi-fluid analysis. Therefore, a system of coupled differential equations is achieved, which describes the linear and nonlinear properties of Alfvén/ion-cyclotron waves in parallel propagation with an arbitrary finite amplitude. This derived system of differential equations is then used to analyze the dispersion properties of weakly-compressive high-frequency waves, which are superposed on a low-frequency Alfvén/ion-cyclotron wave. In a certain parameter range, a wave instability is found, which can be interpreted as a linear spectral transfer process due to the non-uniform background of the low-frequency wave. A particular example for a nonlinear spectral transfer process is the parametric decay of a monochromatic plasma wave. It is treated in a two-dimensional numerical study using a hybrid code. The same code is then used to analyze the spectral transfer from an initially broad turbulent spectrum on low-wavenumber MHD scales into the dispersive kinetic regime, where dissipation of certain wave modes is found. Also here compressive fluctuations grow during the cascade and make a significant contribution to the turbulent spectrum on small scales. The thesis is completed with a general introduction to waves and turbulence in space plasmas and with a basic present [...]