  In future fusion devices fast particles must be well confined in order to
transfer their energy to the background plasma. Magnetohydrodynamic
instabilities like Toroidal Alfv\'en Eigenmodes or core-localized modes such as
Beta Induced Alfv\'en Eigenmodes and Reversed Shear Alfv\'en Eigenmodes, both
driven by fast particles, can lead to significant losses. This is observed in
many ASDEX Upgrade discharges. The present study applies the drift-kinetic
HAGIS code with the aim of understanding the underlying resonance mechanisms,
especially in the presence of multiple modes with different frequencies. Of
particular interest is the resonant interaction of particles simultaneously
with two different modes, referred to as 'double-resonance'. Various mode
overlapping scenarios with different q profiles are considered. It is found
that, depending on the radial mode distance, double-resonance is able to
enhance growth rates as well as mode amplitudes significantly. Surprisingly, no
radial mode overlap is necessary for this effect. Quite the contrary is found:
small radial mode distances can lead to strong nonlinear mode stabilization of
a linearly dominant mode.
