  The collective motion of a finite nuclear system is investigated by numerical
simulation and by linear response theory. Using a pseudo-particle simulation
technique we analyze the giant resonances with a multipole decomposition
scheme. We examine the energy and the damping of different giant collective
modes and obtain the dependence of these quantities on the proton-neutron
ratio. ...(abbreviated) Alternatively the giant collective modes in asymmetric
nuclear matter are investigated within linear response theory including the
collisional correlations via a dynamic relaxation time approximation. For a
multicomponent system we derive a coupled dispersion relation and show that two
sources of coupling appear: (i) a coupling of isoscalar and isovector modes due
to the action of different mean-fields and (ii) an explicit new coupling in
asymmetric matter due to collisional interaction. We show that the latter is
responsible for a new mode arising besides isovector and isoscalar
modes...(abbreviated) Collective motion beyond the linear regime is
demonstrated for the example of large-amplitude isoscalar giant octupole
excitations in finite nuclear systems. Depending on the initial conditions we
observe either clear octupole modes or over-damped octupole modes which decay
immediately into quadrupole ones. This dependence on initial correlations
represents a behaviour beyond linear response.
